As Bongoboy suggests, it could be that the PC has actually 'frozen'. (If so, there are dozens of possible causes). However, the mouse is the first thing to check. Simply unplugging the mouse from your own PC, and connecting it to the kids' PC, will be the easiest way to check. If you need a new mouse, Tesco sell them really cheaply. (�2.29 the last time I bought one).
If it turns out that it's not the mouse, try starting the PC in Safe Mode. (Hold down 'F8' while its booting up). If the mouse then works, simply rebooting it might cure the problem. Otherwise, if the mouse works in Safe Mode but not otherwise, go Start > Run, type 'msconfig' and hit 'Return'. Go to the Startup tab and remove the check marks from alongside any startup program which isn't strictly essential. Click 'Apply', then 'OK' and reboot the computer.
If none of the above works, it's probably time to reinstall Windows.
Chris