I recently built my new computer over the weekend. I have been having this problem where the Graphics Card is powered, but no video was being displayed. At first I thought it might have been the graphics card, so I borrowed my friends GTS 250 and it was the same problem. I am beginning to think that it is the PCI Express slot on the motherboard. I can still RMA it back to Newegg. If anyone of you have had this problem, please let me know what you did to resolve it.
If the card randomly works in the PCI-E slot, and works consistently in another computer, and a new video card exhibits the same problem, it's definitely not the video card. Check your power connections to the video card and reset your CMOS by removing system power and removing the battery. I once saw an Asus board with a bad PCI-E slot do exactly what you're describing. Some boots it would show video to the card, some boots it would completely ignore the card and revert back to onboard video (the card would disappear when in Windows device manager completely).
I have a am2+ socket cpu, that is on a am3/am2+/am2 motherboard. I can't boot it without a graphics card because it has no onboard video. I didn't hear any beeps and both connections are made to motherboard.