It is simple to test then. Since your video card is probably not the problem, take the NIC out. Run at 150 MHz with different CPU burn in programs (Quake3, CPUburn, etc.) for several hours. I tend to do this overnight while I sleep. 8 hours later, if it is still working I call it stable.
If the computer is stable, then it was probably your NIC. If not, then you know it is probably your RAM.