PS/2, USB, or Wireless?
Check the socket if PS/2 or USB... as dirt, and bent parts can cause the problem. If wireless, throw it away, as its useful product life is less than 90 days.
You can sometimes download a new chipset driver set, and reinstall them to fix some problems...
But the mystery is that it works on another desktop and not in the Dell... that makes it be the Dell desktop that has a problem, and socket problems are common, but can be fixed with a can of dust off and alcohol qtips.