Hello, long time reader i figured ill register to give you my input
I had the same problem for a long time.
My setup was a MSI K9A mobo, AMD 6000+ x2 , corsair 650w PSU and a Powercolor 3870
It took me a long time to figure it out even though im still not sure what the cause was...
From the very moment i assembled my new PC it wouldnt boot at all, no signal on my screen but all the fans were running, if you waited several minutes screen would suddenly pop up with the windows loading screen on it, so i figured something during the early boot stages went wrong, i pulled out for example my USB stick, disable USB stick booting or any other devices in the BIOS and it would work again.IT would go well for a long time, sometimes weeks and then it all came back with the same problems.
second problem i had was my PC crashing during gaming, especially when alt tabbing my screen would freeze, 5 seconds later it would artifact and go black on the screen...
both problems made me turn the PSU on and off alot, which eventually made it die completely, i dont know if it was already unstable and dying with me turning it on and off alot finishing it off completely. Being unable to wait on a replacement i bought a OCZ 700w PSU which seemed to fix the crash problems, at least it was alot less frequent.
Till one day my PC wouldnt boot anymore at all, i put my 3870 into my brothers computer who has the exact same mainboard, and it started up perfectly.
Got myself again a new MSI K9A and it started up right away, and never had that problem again.
was an expensive and frustrating adventure, i dont know if it was the new Mobo/PSU combo that fixed it, but thats the best info i can give you so i would suggest trying other(better) PSUs and mainboard if thats possible to rule out card problems.
Good luck!