If the GPU/video controller was defective you would have no external video so I doubt replacing the video controller would fix things here. You likely have either a CFL issue or the inverter has gone.
Whats odd here is Profile doesn't show your display. Are you sure you were looking under the right heading '''Graphics/Displays''' Click on the heading and it should show info for both displays iMac and External.
Have you tried running [http://support.apple.com/kb/HT1509|Apple Hardware Test]?
Looking at your display at an angle you should see a faint image of your desktop (with laptops you can often use a flashlight to shine through the Apple logo here you can't). If you can then you have video only the lighting of the display has a problem.