it does sound like hardware, if user swears nothing has changed, carefully check all settings in BIOS. perhaps you will see system shutdown configured to occur in the event, say, of the processor overheating. or having some other major error. if that is the case, you can change the BIOS setting to try to 'allow' the system to fail without shutdown and get a better idea of cause...
i would also open box and just have a close look. do fans spin? does ram wiggle? maybe reseat ram and processor and video card...
otherwise I agree with charles, sounds like it is going into hibernate. or something is overheating. check to see that all fans are spinning everywhere...
other and weirder things besides misconfigured BIOS can cause systems to not come out of hibernate...like out of date BIOS firmware, video and network drivers, motherboard drivers...also incompatible programs...check whatever you can for compatiblility and latest versions. especially anti-virus, system utilites, cd burner software and all your drivers.
if none of these suggestions help, write again with what all you have tried, system brand and/or motherboard brand. include operating system version and service pack level and what history you may know (specifically, has it been upgraded to its current os and from what previous os)
for example, xp has