A couple of years on, I have an A200 that is just randomly freezing, no errors as such, just walk away, come back and it has either frozen or shut down.
Tried lots of things including new hard drive, new memory, new operating system (Win 8), then read this forum.
I removed the battery, and stress tested the PC for 15 minutes, no problems, and left it running on the bench and it has been running for 48 hours and hasn't missed a beat.
My guess is when the battery dies, it shorts out somehow, and causes the fault. Interestly the battery still holds charge, although not for a very long period of time.
THANKS for the good advice David.