Has anyone repaired graphics issues successfully?

My late 2006 20" intel core 2 duo 2.16 Ghz imac started overheating a couple of years ago, and I've blown out all the dust, replaced the drive and installed smcfancontrol to keep an eye on temps and help keep it cool. That worked until a month ago, when it started crashing, freezing and the display broke up into exploding shards of doom - first horizontal lines, then blocks and diagonal pieces dropped out, now I get smeary weirdness and it's no longer booting. While it was overheating, I ran it as a target drive for two days while cloning the drive and trying to find software problems. I suspect it overheated enough to do more damage, and I'm trying to determine if there's any hope for repair now.

Looking at previous threads, I've taken it apart to blow out the fans, but didn't remove the logic board yet. It's currently sitting reassembled but with front bezel off, which shows me only the first 2 LEDs light up when the power button is pressed. With the bezel back on, it tries to boot but can't display properly. Without the bezel, I get a flashing power light, two LEDs and nothing onscreen. The only docs I could find for what the LEDs should tell me shows 4 LEDs; there are only 3 on this board.