I agree with Bloom's assesment.
Heat is another possible problem. Try running with the side off of the thing and a desk fan blasting at it. At the least, that is a simple way to eliminate heat as the cause.
You DO have a 300 watt power supply right? If not, that could be the culprit.
Also, if you have anything overclocked... try turning it back down to stock.
If that mainboard will take SDRAM, that's your cheapest and best upgrade for sure. You can get a good 256 meg stick of Cas2 PC133 for ... well way cheap. What like $50 in the US now?
If it won't take SDRAM... look at rebuilding a new box.
FYI, the Celly 366 will OC pretty well on a good mainboard and a good Heatsink/fan. My home server runs dual Celeron 366's on an Abit BP6 board with both of 'em overclocked to 500.

It runs Win2k and has been up for 2-3 months at a time without a reboot or a problem.