Only the mouse, or the complete computer ?
You could begin by looking in the Task Manager (Ctrl-Alt-Suppr then Task Manager) if a task eats Cpu time.
What do the temperatures say, including at the graphics card? Your fingers give a first indication, specialized software a more accurate one. Look at dust in the coolers then.
Also, enter MsConfig (doesn't exist on W2k initially, Microsoft recommends borrowing it from Xp, look on the Net) and eject the tasks that shouldn't be there.
Have you tried to boot a live Cd, like Ubuntu or Knoppix? If the same happens, it will be a hardware problem, for instance bad cooling.