PC133 should still run with no problems at 100MHz. Might be a memory problem though - try
www.memtest86.com.
At a rough guess you have most likely got a problem with overheating. Either the memory, processor or graphics card. A simple memory/processor error would cause it to lock up/error - resetting would then clear the memory and you be waiting for the next memory/processor error to freeze it again.
I'd suggest (once again) reseating the heatsink on the processor - possibly using some thermal paste as a conductor - and the next time it locks up got into the bios and have a look at what the temperature is - usually in hardware monitoring.
The 10-15 minutes thing would be because a lot of processor activity (and Heat) will be generated by using a software modem, displaying web pages etc. The same would be true of playing Quake.
The reason I think it's more likely to be the processor/memory/motherboard chips overheating is that you don't mention any graphics glitches which would point to a Graphics card problem.
Might be worth you:
a. Checking to make sure the fan on the heatsink is spinning (had that happen once)
b. Chuck one of those exhaust blower fans into the case.
As to the modem - does just sound like an unfortunate coincidence.