This may or may not be your problem, but it sound very similar to some
tests I ran.
I had this similar problem, but created it myself while expirementing with
overclocking Pentium chips (making them run faster than advertised). I had
a P150 overclocked at 180MHz and it ran fine for about two weeks then I got
the black screen. Three weeks later same thing, then two weeks, etc.... I
got the same results from a P166 clocked at 200MHz. Check your CPU chip.
If it has a black sticker (or any sticker) on it covering the real speed,
it is an overclocked chip (this happens more than you would think.) These
overclocked chips will run for awhile before crashing on a cheap
motherboard, and will run forever on an expensive one (check your CPU
anyway, many store bought systems are overclocked!). This mostly applies
to Pentium class chips, not AMD since they are already at their maximum.
More info about overclocking at:
http://sysdoc.pair.com/overclock.html
BTW: I have a P166 clocked at 200MHz and running fine as long as it is kept
very cool. No extra cooling and I get the black screen sometime later (days
or sometime weeks later).