For the last two years, those Keyboard and Mice that were bundled with my HP PC served me well. Lately, I've had this problem of both of them not working. The keyboard just randomly stopped working today. The dongle's connected, but neither of them work. The dongle doesn't even detect the Keyboard anymore. Lol, the mouse is working, I just checked, but it's being really crappy. The left mouse button doesn't always respond. Although, I dropped the mouse a bunch of times but it kept working so I think this will fix itself. Still, I have the problem with the keyboard.
New keyboards and mice are cheap. Have you tried replacing them? You should be able to verify both the keyboard and mice rahter easily.
Why didn't you tell us in your first post that this was a wireless keyboard/mouse???? Yes, I finally figured out by your (incorrect) use of the term dongle. The troubleshooting procedure would be a little different in that case.