Do I have bad RAM (DDR)?           

If the BIOS posts ERROR codes or beep codes, or CAP's lock LED blink codes say RAM is bad, it is for sure, (see 1 exeption)  Those beeps did  not lie to you.
I will give only DDR2 examples, DDR3 is near same rules, but are unique sticks for DDR2 systems only (but the rules of the game are the same)
This happens most the time buying new ram or having no ram at all and buying it or upgrading ram. (I will not go in to buying counterfeit ram off  fleabay = any internet auction site on earth)
Test each stick 1 by 1 in bank 0 or channel A to see which sticks are good or bad!
What is there to get wrong, for sure looks don't matter aside from tag partnumber or chip partnumbers.
Do not buy unbranded chips, a.k.a: No NAME.  The Kington and Crutial or Hynix, or Samsung, or OEM brands like HP or dell are good, but maybe brand called "SOM Ting Wong"?
Rule #2 is buy them (kits) in matching set if you know what is good for you, do so.

The speed must be a matched or better. See wiki on topic. (PC2-6400?)
The CAS spec, needs to be lowest number at recommended OEM PC makers  spec, and is best of all sticks have the same CAS spec.  (matching CAS and faster CAS is always ok, CAS lower numbers are faster)
The maker "OEM" of your PC tells you what RAM you need, and there rules are the only rules that matter, not intels, not AMD , not anyone else.
Next is the BIOS may need upgrading if your old 2003 PC is stuffed full of 2018 memory it can fail. (BIOS beeping like mad   POST code errors for bad / wrong ram or missing ram?.)
Example #1: PC2-6400 4-4-4 (common DDR2 spec)
Most ram on home PCs use unbuffered non ECC ram. (unlike what real servers use or real workstations use)

Factors: DDR2, Density, speed (PC2#), CAS,pin count , and voltage mine must be 1.8v, DDR2 pin notch in correct spot, and do not force the card in backwards. (do not mix Laptop and desktop DDR)
Keep in mind Fleabay DDR can have the  wrong photo shown, (called stock photo, horrors) and sell you RAM that is not for you PC.

Your PC has  max memory SIZE allowed per DDR slot and for all slots added up total, this is  in your OEM  PC model. spec. and service guide.

Last is the odd words DENSITY.
Keep in mind Density relates to   HISTORY and is  SNAP shot in time, back long ago chips were low density,  unlike today.
So density is  relative term, (time wise) lets freeze total stick size at 1GB to make this more simple. 
There are 2 things here, CHIP (those back things soldered to the STICK) and the PCB Card stick is the other thing that has density.
The CHIP has bit density (low and high) old is low, today is high. 
The stick with lots of green space and backside devoid of chips is low density STICK , (modern) The stick with 32chips 16x2 , is old High density sticks.
The PCs BIOS and MMU (and mobo design engineer) is what limits density, (your OEM limits this , like DELL or HP) 
The MMU used are vast,  inside the CPU is the MMU or many times the CPU has no MMU but uses  Northbridge chip to connect to memory banks. (all these things have limits)
Some old Gforce chips were very limited as were Intel chips early on. (for this rule of density and max size too)
The stick in your hand can have 4 chips there or 32. (16 front and 16 year)
4 chips is super low density sticks, lots of green space,  the chip however are highdensity chips, look like the below photo #1
Some sticks have 4 chip front and no chips rear, those are low density sticks,  (means less chips there)
The low density sticks all have high density CHIPS. 
Cost is not a matter here  after all we are talking 2003 to 2018 (now) and many chips made then are not even made now in 2018, but the sticks are sold from Old stock sticks or made from old stock chips.
The Cost of some old high density sticks can be very expensive just for the RARITY factor. (and scalpers are everywhere today)
If you let price become #1 in your buying choice you will get bad sticks, (wrong for your PC)
Other factors can cause failure. (and expections)
  1. Your BIOS scans the SPD chip and and can not understand the ID message from 2018 back to BIOS made in 2003, and fails and beeps, even if the RAM is 100% perfectly good and usable.
  2. The MMU on your mobo can in fact not like your chips (AMD NForce tops the list here) Memory manager unit (chip or part of intel processor)
  3. The PSU can be bad, has huge noise due to say 13 year old  relic bad CAP.s inside the PSU.  50mV is max, see ripple. here. (if you see huge  40kHz ripple there the PSU is bad)
All the below is to get the Idea of what Density means.

Low density chips make for high density sticks. (too many chips , 32 below in fact)
It is DENSE STICK with too many  chips is the correct way to say this.
In the old days chip density was poor "low" (total bit count per chip low) but decade later chips are no way more dense thinks to... (Google  G. Moore's LAW, of Intel fame to know why?)
Photo #1:
This class of stick can have just 8 chips today 2018, front side only. (not 32 like the below) My guess is this stick is 2003 made.
That tiny SPD chip here is the PnP , the who are you chip ,that BIOS scans.
Best is to upgrade your BIOS first. If you can. (using an old working 256 or 512MB stick.)
Samsung chip maker makes some of the most dense and fast DDR chips on earth.
four gigabit per chip. (as does Hynix or Micron)
Here is but one example for  cheap desktops 8GB x2 is top of the mark.

2018  new 8GB DDR4-2133 RAM 1.2vdc
Only 4 chips, for this monistor, so is a low density STICK but very high density Hynix(tm) chips. Sold by HP or Crucial.  (using 8 Gib DDR4  chip density level at 20nm process)
In April 2016, Samsung announced that they had begun to mass-produce DRAM on a "10 nm-class" process !  (G. Moores law in action here)
The stick below has only 4 chips, (chips means descrete integrated electronics or ICs)  If you buy 2 sticks, you get a full 16GB of RAM  for say windows 64bit.

What do they do when G. Moore law runs out of steam?
Will be first seen in high end servers and many soon PCs. (workstations)
The makers use a new  3D Die stacking, here is 4 high. 32Gbit chips at 

Links  to simple DDR facts.   In each case of the below your motherboard dictates what you must use.
  • Unbuffered Ram or  buffered) Most cheap PCs use unbuffered ram.

  • Registered (does not mean licensed but is data latch register  logic)

  • ECC Ram ( as seen in all top  servers)

DDR memory density links pretty good.(desktops only , laptops and servers have there own class of processor and ICM , MCM usage)
Best post on old motherboards by anyone is here: excerpted.(and corrected using italics)
"Now specifically with high density ram:
The old nothrbrige chipsets for intel never supported these new DDR chip configuration of high density modules, ASUS boards for even AMD never supported these new modules, only select few boards made the northbridge capable of supporting it.
There are several fleabay stores   that even stated in the fine print that it won't work on intel systems."
My comments:
The Northbridge can be a Mobo chip "MCU" or  later moved inside the processor , nForce on board is one of the worst ever NOW!. (and supported ended on them at w8 or W10)
The Northbridge hardware sets a logic limit, (address decoders) and the BIOS on all PCs can reject DDR at first blink for a fact ( if not BIOS upgraded)
What is Northbridge, well here is 1 example before Intel went to advanced Processors with advanced DDR support on die, with 1 die not 2 dies, the best Intel computers start here , in my opinion.
Called ICM Integrated System Memory DRAM Controller . The first was in the year .... end of 2008 at Nehalem, with DDR3 direct support)
November 17, 2008, built on a 45 nm process and used in the Core i7, Core i5, Core i3 microprocessors. Incorporates the memory controller into the CPU die. ( a huge Mile stone this)
The Intel processors with DDR via  MCH started in the year 2002.  with MCH seen below.
 RDRAM before that (forget RDRAM) the first chip  was 845 chipset + old AGP + DDR (MCH). (dual channel and up to 4GB ram) 900 series began DDR2.
Let me forget nForce, totally it is useless today, lacking drivers modern, lets focus on Intel only memory logic, and this is the first one from Intel 16 years ago (2002) .
To learn what your DDR can do or can't do read the data sheet on MCH or if Hehalem or newer processor, read that.
I read the data sheet first, like the below photo came from and that ask my OEM what My PC can do, for sure the hardware limits WIN FIRST , OK? (then mobo limits and last BIOS)

Page 9  in the Intel 845 data sheet is clear, per below on DDR. Focusing on MAX limits only.
( this is just 1 example of one chip MCH 2002 year so if you want to learn what your PC can do , learn what MCH you have then read your matching datasheet, ) 
First learn that DRAM chips are sold in Mb (megabits not bytes) but sticks (now) are sold in GB sizes. (x8 gives you bits)
Below is strictly DDR limit not limits for ROM Firmware ,etc.
  • 266 MHz Double Data Rate (DDR)
  • 64 Mb, 128 Mb, 256 Mb and 512 Mb (Mb means MegaBit not byte) the 512s are 1GB sticks. x2.  (GB is GigaBytes) so 512GB divided by 8bits is 64MB size chip, so  x16 chips is 16x64 and is 1GB stick.
    technologies for x8 and x16 devices (devices jargon means, DDR actual chips)
  • Page sizes of 2 KB, 4 KB, 8 KB and 16 KB

  • Maximum of 2 Double-Sided DIMMs  (2 slots)
    (4 rows populated)
  • 2 GB Maximum using 512 Mb technology (that means 2 sticks of 1GB is the limit) so that means 1 stick is 1GB limit. 2x1GB.

The First processor and best ever with DDR direct (ICM) is Bloomfield 2008, with CPU # 920, 940, and 965 on top lid marked that way, called GEN 0. or first gen.
DDR3 and 24GB limits. some  can do 32GB, (read your exact model processor and look it up)
Block diagram of it is below. Just CPU die. 130watt of heat possible.! See here for great report on 920's

This is CPU Gen 1 920 processsors. (family)  This is one of the frist great processors 2008

version 1.  11-1-2018