Check the QVL list to see what BIOS revision is required for that board to support the FX-8120. If you've got something earlier, you might be able to take it to a local computer shop to get it flashed for a small fee (unless you want to buy a cheap AM3 CPU to do it yourself).
I think your power supply is underpowered for your build. DO you have access to a 700 watt PSU? That is what I would check first.
Otherwise by my experience the symptoms you describe indicate a possible DOA mother board. Seen it many times, if the fans and/or LED's are running but no post activity than that is typically a MOBO issue. You should get a stronger PSU regardless.
Consider that your CPU uses 125 watts of your 500 by itself, than the video card will suck down quite a bit, other peripherals etc.
It's not the bios version, because according to the list, this cpu is supported by all versions: http://www.asrock.com/mb/AMD/970%20Extreme3/?cat=CPU
Try to boot with only one memory stick and disconnected disks and reset the cmos with the jumper. Maybe that helps.
Your PSU, while not the highest quality out there, should easily power your rig. The HD7750 uses only around 56W running flat-out. I'd be surprised if your rig pulls 300W from the wall.
Check the QVL list first, then go from there.