cpu or memory burned out?

A friend of ours has an ibm thinkpad (model 1492). He leaves the battery
in even though he has the laptop plugged in to the ac transformer. A few
days ago the
computer got left on overnight (he usually turns it off after using it)
and in the morning the battery was dead, even though it was plugged in
to the ac. It took a long time to recharge the battery (after turning
the computer off). Now the computer is having alot of problems freezing
and programs not functioning right.

I tested it booting from the a: drive with a virus-free win98 boot disk
(to the dos prompt) and it still froze after awhile. (It takes maybe 1/2
hour before it starts having problems.)

Could the battery have caused this? There are still problems when the
battery is removed.

Would appreciate any suggestions for programs that could test the cpu
and memory.

Thanks.