I've been using the loghitech MX 1000 laser mouse for about 5 years without any problems until now,
when I fully charge the mouse and connect it back to the receiver, on desktop it displays your MX 1000 laser mouse batteries are critical
yet on the mouse there completely full I'm using setpoint which comes in a disk with your item.
After 5 years it sounds like it just need a new rechargable battery. Though these are considered non-serviceable many solder in a Kodac KLIC-5001 or an NP-60. Be sure to put it in correctly and wear protective gear if you decide to do this yourself.