First things first, I think it's a great idea to introduce your son to alternative operating systems.
Right. In regards to your shutdown issues... questions for you:
1) Is the computer actually shutting down to the point of powering off?
2) Is it simply crashing to a black screen, or to a text-only screen etc.?
If the computer is not completely powered off, is it at all responsive, or completely frozen?
Do your best to verify with your son what site he is visiting/action he is performing when the issue occurs. If the issue really is this repeatable then it should be something the two of you can track down together with a bit of teamwork. Is it a gaming web site? Does it attempt to load animations via Flash or Shockwave? Is he running a 3D game that powers up a 3D video card in the system (not sure what the components are, as you did not specify). Does it happen when he tries to play audio files? etc...
As bizarre as it sounds, I've seen systems freeze or reboot only when running 3D games--turns out these systems had spotty power supplies that became very unstable when run near the maximum wattage.
As this particular computer was cobbled together from various parts and pieces, there's a chance this is hardware-related, so that's worth considering.
The two most likely culprits, in my experience, could be the RAM/memory and the power supply. A distant third might be the motherboard.
To test the RAM, an easy way is to run MemTest86 on the computer. This is a very small, non-interactive program designed to stress out all system memory, and is included on many current Linux distribution CD's. It might very well be present on your OpenSuSE 11.1 installation media, in which case simply boot the machine off that CD/DVD, and select the MemTest86 option.
If it's not on the OpenSuSE 11.1 media, download the latest release (v3.5) from the MemTest86 home page at http://www.memtest86.com/download.html
You can make a bootable floppy or CD, depending on which you wish to use... In either case, once you have MemTest86 available, boot the computer with the floppy or CD you create, and let the machine it overnight. If there are no errors, its unlikely (but not impossible) the issue has something to do with the RAM in the computer.
If there are errors, however, I recommend removing a DIMM and re-running the test. For instance, if there are two memory DIMM's installed, remove one and re-test. If it fails again, replace that one with the original DIMM and run again. If it doesn't fail, you have isolated the bad memory module. If it fails again, you may have two bad memory modules... or an unreliable power supply or motherboard.
The next thing I would try is another power supply. Cheap, off-brand power supplies (especially older, used ones) can cause all sorts of system stability issues. If you have a spare I'd recommend swapping it out and seeing how the system works then.
Sorry for all the text.
Hope this helps you get started on the right track to finding a solution.