hi ive just signed up due to this issue, never had a gfx card fail on me but now have 2 in as many weeks.
my system :-
Athlon 64 fx62 dual core
Asrock Alivexfire esata2
4x1gb ddr2 800
1tb seagate sata hdd
300gb ide hdd
and a 8600gt with a busted fan working on a ACE black 600watt atx 2.03 psu.
The GFX in question are a BFG 8800gtOC 512mb, which i installed and got no signal but the fan powered up and stayed constant 100% speed.
The second is a hd3650 which i got just so i could play somethin til i sorted the 8800 out, this worked fine for 3-4hrs and then same symptons came up, Ive tried it on a ASUS M2N NM/s board and same problem although i have gotten a signal a couple of times on that but only for post and a few seconds on desktop.
Tried breadboard, everything ok until i put the 3650 in, 1 long beep with 3 quick ones. i think ive been seriously unlucky and got 2 cards as they bit the dust. I cant see it being anything else as the 8600gt still works fine.