It could be the battery or the power converter in the computer.
But after a closer reading it sounds more like a chipset error.
Does it work if the battery is completely removed and you boot on just the power cable?
On this link you can find the latest drivers for the chipset:
I can also see that it is an older model. You don't mention what version of windows you are running, but if you are running XP or earlier that says something about the age of the thing.
It could be that it is just simply worn out.
Luckily almost all the Thinkpad models are build to last, so you could take it to a shop and have them run a diagnostics on it and replace what ever parts that might be failing.
Just be adviced that the price for the diagnostics would most likely exceed the value of the laptop.
Personally I would get a tech savvy person to get the harddrive out (myself in my case), plug it to a second device with cables as an external drive (can be bought in most wellstocked computer hardware stores) and then do a backup of any essential data.