I just got a new psu and the Sapphire 4870. When putting everything together i my computer shorts only turning on for a sec then going off. I tried another psu, the ram, and pretty much everything besides a different mobo. When i only hook up the drives, 2 sticks of ram, and processor, it will boot up but once my card is in it does the same thing.
I did get it to boot up once with the card, but it is very wobbily in the pci slot and once it wiggled it shorted. I have a Corsair 650 and a MSI-RS482m4 which is a pretty old board.
NEVER, EVER move, or attempt to move, wiggle or disconnect ANY part of a running PC. ALWAYS power it down and remove the power lead beforehand or you risk toasting the whole thing!
You really need to secure that card fully using a small screw to lock it into place to stop it wobbling. The 4870 (at least mine is) can be a heavy card and just dangling it off the slot will most likely force it out of line and cause some of the contacts to lose contact.
The screws can be obtained off the `net or from a local pc store.