Welcome to the Forum, James!
First, did you check if your T41p is still under warranty? (check this at
Warranty Lookup). If not, and while I don't have any "I know exactly what is wrong" explanation to the problem you describe, I would nevertheless suggest the following to try hunt down the source of the error:
If you are able to (as I understand you are?) boot from a CD-ROM, I would strongly suggest you try all the following:
1) Download and burn a bootable CD-ROM with
PC Doctor for DOS bootable CD - ThinkPad - and run it
numerous times. Note that there was just released a new version of the Lenovo "PC Doctor" - see
Which PC Doctor for T41p? - but I am not quite sure if it will run from a CD-ROM?
2) Download, burn a bootable CD-ROM with
memtest86+ - and run it
numerous times.
3) Consider enabling "Extended Memory Test" in the BIOS; see where in the
BIOS simulator - ThinkPad T42/p with fingerprint reader (--> Config --> Memory) - I guess the same would apply to T41p's.
As
schen just mentioned, there is a chance that you have been hit by the "loose GPU" syndrome; see the sticky
T42 shuts down when i move it.
Johan