Stop the Stop Commands!

[Distressed]

Alright so i have had this problem for a while now and it is really getting bad.  My laptop will randomly shut off or go to that 'blue screen of death' where it tells me it recieved a stop command or error and that there is something wrong with a new hardware installation.  The only hardware I have put in was RAM that needed to be replaced because of bad sticks.  I know its in there right and thats not the problem.  I put in a brand new stick and the problems i previously had were significantly reduced but now my computer will often randomly shut off and occasionally wont restart for a short time period.  Please help me, my other computer tech friends have so far been unable to fix it.

[GX1_Man]

Ummmm, do we get to know any specifics about the machine, age of it, operating system, or we just have to guess?  

[Distressed]

Sorry, I was really trying to write it all down before it shut off and i forgot the specifics.  
Ok so its a Intel pentium III IBM Thinkpad with Windows XP.  I think its a 2002.  It has 384 MB of RAM.
I have also found that running GAIM significantly encourages occurances of automatic shutdowns and makes it alot harder to get the computer restarted, if that helps at all.
If there is anything else you need to know just tell me.  I would very much appreciate any help.  

[GX1_Man]

A Pentium III probably did not come with XP. Has it ever worked correctly with this O/S. Are we sure it is clean from malware/virii? Have you tested the RAM (www.memtest86.com) and the hard drive diagnostics from the IBM site or the manufacturer's web site (free downloads there, too.) Is the battery in good shape with no signs of injury? Same for the power adapter?

I would start with the diagnostics (you do have a floppy drive, right? Also, if you could post the 7 digit machine code (XXXX-XXX) from the bottom of the machine, we could identify what is is really comprised of.