Yes, sounds like a driver, doesn't it? Try deleting the mouse and re-booting; Windows will re-install a driver - which might not be the same wrong one. Well, it's a start.
As to removing the battery: doesn't the machine shut down if you hold down the power button for (typically 7 but perhaps) 10 seconds or more. Have you tried that one? This has worked for all my various m/cs for 15 years or moren.