Laptop keeps powering off

So a few months ago my father in law gave me 2 toshiba laptops he no longer needed. The newer of the two had a broken screen but was otherwise fine. The older one had a bad cd-rom. He already had a new one so his thought was, swap out the cd-rom and you have an old but working laptop. Well, I am working on just getting the old one cleaned up and usable however the blooding thing keeps powering off on me. I've had it plugged into the charger for a couple hours and although the battery was completely dead on boot it is taking a charge. The C-mos battery was also dead so all time was wiped. I can get it to boot and generally get some programs going but it seems to shut down between 10 minutes and an hour into an activity. So far I've just been trying to get windows updates going and spybot to run. Should I be looking at power loss to the laptop or heat issues? The bottom does not seem hot and I believe the ram is alright but I haven't checked anything out to deep. I was planning on just reinstalling Xp on it but I'm not going to start it if there's a bigger hardware issue. Anyone has any ideas on what I should look at? programs I should run to test? Thanks.

Toshiba 5005-S504
Part No PS500U-00Y0LX (trying to find model)
Sadly it's running a P3.

Is this thing even worth saving to use, should anyone know the specific type of laptop. The newer one is a Toshiba Satellite M55-S3291. Be really nice if I could just swap the boards out.

Well right now I can't even get into the bios. If I am finding the write key by accident the only option I have is to hit F1 to reset to default. It loads and runs, I just can't tell why it's shutting off. Bad battery? Which is taking a charge, or if it's something else. Key thing is, given how old it is, is it even going to be worth spending the money for a new Cmos and laptop battery. I would say no.