Ask yourself what changed when the problem first occurred.
Don't think changing the BIOS will do anything as it wasn't broke to begin with.
Sounds like an intermittent H/W failure. If I had the same issue I would download some benchmarking software that runs H/W tests over a long period of time, if that doesn't catch it, I would start pulling out bits of hardware until left with the bare minimum. If that doesn't catch it then I would start looking at a new PC as you should have been able to depreciate this one on tax by now.