Don't take this the wrong way but have you connected both power leads to the card? It's one of the most common issues (and it's nice to know I'm not the only scatterbrain who does it).
Sounds like a driver issue.
First download and save the latest WHQL drivers from the AMD site, don't use Beta drivers and don't download from anywhere else.
If you have any tweaking software like Afterburner or Precision installed, uninstall it and delete any profiles when asked.
If there's no change try this:
Uninstall the current drivers and use the drivercleaner to clear up the mess.
Manually go through the system and delete anything left over.
Install the drivers you downloaded earlier.