is it a ps2 connection? They you have to restart the computer for the mouse and keyboard to work. If its USB make sure the usb ports are working, and you have installed any software you might get with the mouse and keyboard
Search for the drivers on the internet for that make/model, and make sure they are installed correctly(for usb ones).
Check if it works with the computer you're currently using. Also check for updates ( Go to Control Panel > System > Hardware Tab > Device Manager > Find -Keyboards, right click it, Properties > Update Driver and then -Mouse or Mice (for some) right click again, Properties > Update Driver) (<-- Just in case ^_^). If not then , I'm gonna have to go with the mo'bo.
the mouse and keyboard work with my one computer and not with the other, and i cant update the drivers because i cant use my mouse!