it seems to me the PSU could not provide enough power to your system. if you have other card lying around you can try to use it and see if your system able to boot up. it could be your PSU or your GTX580 is DOA. have you tried disabled your IGP via BIOS?
You read my mind renz about the PSU. I couldn't find another card to plug in but here's what I found interesting. When I plug in both the 8 and 6 pin, no boot (580 fan doesn't go on). If I leave the 8 pin plugged in only (pull out the 6 pin), the 580's fan churns and the computer boots. If I leave the 6 pin plugged in only (pull out the 8 pin), the computer boots (580 doesn't do anything). I think the PSU is not providing enough power. I thought 850W would've been enough but that may not be the case.
with 850w PSU you should be able to power up two GTX580. in your case the card should be able to boot up if one of the PCIE power connector is taken out which is weird. maybe the card needs a check as well
Attach graphics card with your system and Go to bios setup and Turn off built-in video, and enable "PCI x16 2.0" then turn off your computer. Attach display cable with graphics card and start the computer.
Note: Built-in video option must be in "Boot configuration" option
and "PCI x16 2.0" must be in "Video configuration" option.