I don't mean to skip all troubleshooting steps, but whenever I find odd problems on a computer that has a Cyrix, the first thing we do is swap the processor. Most of the time, the problems dissappear.
Again, this is not "proper" troubleshooting, it is just my experience with the cyrix processors around that speed range. This is especially true if you found your CPU fan to be dead (or nearly dead) at any time (these CPUs got really hot really fast).
You might run CPU diagnostics, but to be fair, the problem could just as easily be *deep breath* corrupted software, bad video, bad RAM, bad MB, bad sector on the hard drive, bad power supply, etc., etc., etc. ...... I suppose that if we ignore the CPU, I would try swapping the video, then RAM, then PSU to see if the problems go away (these are usually the easiest to swap for most folks). To test for software issues, you could do a temporary install on a spare hard drive and see if the problems return.
I hope that this helps!
Mudskipper
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Groucho said it best- "A four year-old child could understand this!
Quick! Run out and find me a four year-old child: I can't make heads nor tails out of this!"
