Problems, with Wireless Keyboards and or mice or combo's           

Both devices have batteries, and is the number one reason for dead devices or acting STRANGE in any way. The 2 batteries add up to 3volts below 2vdc the manual tells you it fails.
The first wireless keyboards and mice started long ago, at maker  around year 2001. (yeah 2 decades ago) (some HP call CORDLESS !)  (Oldest is see is the P5911a ,circa 2001 manual only)
HP has many new keyboards seen here at Walmart.      or this LV290
All wireless use these ways  to communicate the matched receiver device.
IR (infra red, just like your  TV remote works) and is 100% custom design , not any standard and you can not mix up parts.
RF means , radio,  this is wifi, bluetooth or 2.4GHz custom receivers, and can never be mixed or mixing makers either.
Just because the book on it stated 2.4GHz this is not 801-wifi, not at all. It is custom HP designs, non standard.
Modern PCs mostly do use BT , due to short range and using codes to prevent 1000's users in one room (insurance claim centers?) and not have users  interference,) The codes can not be changed.
Modern keyboards like this are now encrypted so others can not watch what you type (hackers). (security )
The receiver might  be BT bluetooth, but uses 1 to 9999 codes custom you  makers set of devices never to be mixed. DO NO LOSE YOUR RECEIVER. (Dongle)
Do not mix receivers, nor makers nor brands nor models. ever.

The below is the keyboard, Receiver Dongle (RF) and the mouse,  they are a matched pair.
Super relic example #1: (something that did not explode in Y2K panic!) 

The old relic  HP models 5187 or 5219crf/urf are 20 years old.(no w10 support)  8 meter range.(26ft) or 2004 Keyboard(UH0G)/Mouse(MH0GC)/Dongle(DHN0)
There are 10 years (for sure old) of HP keyboard that are not support by HP now nor MS Windows 10. 2010 or older may be zero support. (ask your PC maker or you keyboard maker for help!)
HP has a horrible web site (IMO) that does not even mention models in this link!, of keyboards, nor any support on old keyboards. but HP  does have support  on this., sold here   K2500.
The HP search page finds no keyboards using any numbering conventions seen on the device service tags.  (none of the KG-0851 shows nothing) 
I learned later that only google finds things inside HP's horrible web pages, for some things, and keyboards at HP are NOT indexed in the correct why, like all else there.

Here is  list of failures.
  • The batteries if dead or near dead in either the mouse and keyboard. Battery life stated in most HP manuals show 6 months, (less for cheap carbon batteries imported sold for 4 for $1)
  • You lost the Receiver, (a.k.a, dongle or USB receiver, some huge seen above or super tiny, USB thumb nail device.
  • Do not mix parts from different makers of devices here,  for sure makers name. HP must be HP , Dell must be Dell and the right match by models, vast models exist !
  • The mouse on some come new with hidden compartment that stores this dinky USB receiver. remove it and put it in your PCs USB port.
  • The 2 main devices may have an on/off switches (to save battery life) turn them both on.
  • Not doing the Pairing steps in your manual even the old 5219 must be paired, for fail you will. The keyboard and mouse must be paired. (RTM) The newer drivices are auto paired,with true plug and play.
  • If the old devices 20years old are no good now. Buy  a new one for say $20 (a set)
  • Watch out for this, some sets, the mouse talks to the keyboard, wireless then the keyboard relays that to the PC, so if the keyboard is dead, then the mouse,  in this case goes dead with it.
  • The mouse can get dirty so clean the optical paths . (jumpy mouse?)
  • To go longer life span, run lithium batteries (non rechargeable).  like this, AAA.(4 times longer)
  • Some newer devices have built-in rechargeable batteries, a cable used that does that. (so you are offline until it charges backup , that stinks!?)

Why not just get a better keyboard, wired never fails, but here are some good wireless sets. MK235? (and longer lasting batteries)

The new HP devices, wireless KBD/mouse.  (the manual with it (K2500) is written for only visual klingon's, horrid !) but far far better is this page.(even covers old dongles with a +-connect button)

version 1.  12-16-2019