What are your computers specifications? Processor, Memory, Hard Disk, etc...
If you have less than 2GHz Processor or 2GB RAM then maybe that's it, or possibly a Hard Disk Drive failure caused by system modification or a dormant virus. Power Supply might not be enough for the extra load although that seems unlikely I'd check for it anyway if you upgraded anything else like Graphics, Extra HDD's, or componets could drain the available power.
Is it a RF or Infrared LED or Bluetooth Wireless? Did you check the batteries?
Have you done anything else recently before the Keyboard and Mouse upgrade?
Downloaded programs, music, or videos could have had viruses, Spy/Mal - Ware could have corrupted your critical system files
Was your old Mouse and Keyboard PS/2 or USB and do you have another PC to test parts for diagnostic purposes?
Check the Hard Drive Disk in another computer as the second Drive but first run a Virus Scan, Scan Disk, and then Back up your Data. Also try the other Mouse Keyboard either USB or PS/2 whichever you didn't have in the first two. Also try the Mouse/Keyboard on another computer after backing it up as well and try the drivers and software from the manufacturer's website instead of the included disk as it may have been corrupted as well, you never know.
That is a tough one but those are the steps I'd take although not necessarily in that order
1. Check components on another PC
2. First the mouse/keyboard
3. Then remove any unnecessary Components from your problem PC
4. then Virus scan and Spy/Mal - Ware removal
5. Try a new Mouse Keyboard combo from a different Manufacturer but same connection type as the one that started the trouble
6. as a last resort, Format the Hard Drive, do a Clean Install of your OS of choice, update with latest drivers, then install the Problem Components with downloaded drivers from their respective websites and Retest for any issues
That's the best I can do with the info you have left here, Try it carefully and completely, then report your findings to better address the issue, Good Luck