JNHARRINGTON's problem did turn out to be the inverter board. Flipping the board end for end as in one of my other posts made the darkness move from top to bottom and did verify the issue
to Anro Fosyd:
The inverter lights the bulbs and general screen brightness.
The controller board sends power to the actual screen pixels and lights the individual pixels.
Since you said it does get dim after it gets hot, try unplugging the DVI after the darkness on the screen shows up to get it into the lor test screens and to get a better idea if it is inverter related or the controller.
If after it gets hot and if the darkness does show up in the colored test screens then it may be inverter related (possibly power board related). If the colored test screen are even brightness right after unplugging the DVI then it is probably in the controller.
Since it favors the one side of the screen, and if it is in the controller board, then it is more than likely in the large main chip at the middle of the board.