IBM i Series Thinkpad with power supply problem?

[Guest]

I have an IBM I series thinkpad but when I start it up, it comes on and
after a few seconds, shuts down the power. I can not even turn the
machine back on usually - power button is dead- but after a day or two,
it does come back and this repeats.

Obviosly a hardware problem but how to diagnose, and if too complicated
- where is the best/cheapest way to deal with it (am in SF area if that
matters)?

Thanks!