I had a similar problem. 22" ADC cinema display would go black, and LED power light would stay on solid bright . The display is attached to a G4 Digital Audio (which is connected to an APC 650 UPS). Typically it occurred after a thunderstorm. I found that if I left the Display unplugged for ~3 hours it would start working again when I plugged it in to the PowerMac (I could tell when the display would cooperate again before powering up because the display LED would go from super bright solid, to off).
After it happened 4+ times, I swapped out the original 32MB GeForce 2MX video adapter. Initially I tried a GeForce4 Titanium 128 MB card which worked okay for a while, then the display exhibited the same behavior. Side note: there was zero difference in performance of the Titanium video adapter (either in benchmarks or observations from daily use) from a GeForce2MX!
I acquired a GeForce 4MX 32MB card and haven't had any problems in months. So my suspicion is that 22" ADCs are finicky about what video adapters they are attached to.
