weird boot/video problem, help appreciated!

Hi all,I'm hoping someone might be able to help with this because its
got me absolutely stuck!!

config:-
Abit KX333 mobo
Athlon XP2000
2x 256mb Crucial PC2100 DDR
Sapphire ATI Radeon 9700
Win2000 SP4 (not that I can boot into windows at the moment!!)

I'm having a problem where the PC wont boot, it gives the 1 long, 2
short beep for a video fault, and fails to turn on the monitor. Thing
is, this is intermittent - it first occured a couple of weeks ago and
randomly resolved itself after a few hours. It was then fine for
exactly a week, and happened again, again resolving itself after a few
hours. on both occasions I had been tinkering like mad but hadnt been
able to fix it, and it resolved for no apparent reason when i just
tried turning it on one more time, out of desperation. Nothing had
changed, just like nothing had been changed to make it happen in the
first place. Its now happened again today, and doesnt seem like its
going to get better this time.

I've tried the video card in another mobo, an Abit KT7 that i know to
be good, and it wont boot, with the same beeps. Fine, must be the
video card I thought, so I put a Savage S4 that I know to be good into
my mobo. Makes no difference, still wont boot and still gives the same
error beeps. The only conclusion I can draw from this is that both the
m'board and the vid card have a fault, and that somehow one must have
developed a fault first and damaged the other. That still doesnt
explain the intermittent nature of it, or why the good m'board and vid
card havent been harmed by exposure to the damaged ones.

other things I've tried-
-removing all PCI cards leaving just the video card
-unplugging ide devices
-removing m'board and putting it on cardboard, in case it was
shorting/grounding itself on the case
-reseating the vid card, many times
-changing memory around
-clearing CMOS

As mentioned above, none of this made any difference, and on the
previous occasions I just tried turnig it on having changed nothing
since the last attempt, and it booted fine. Just as suddenly as the
problem appeared, nothing having been changed.

Sorry for the length of this post, and thankyou verymuch to anyone who
can suggst anything!!! At present I'm looking at replacing the mobo
and vid card, which will be *very* expensive.

Cheers