I had this same problem, too. Oddly though, ONLY when he display was connected to my G5 Dual 2.7 tower. When I unplugged the display and immediately plugged it into either my MacBook Pro or my Mac Mini, it would work every time.
I tried all kinds of voodoo with resetting various things on my G5 tower, unplugging/replugging, moving the display power adapter to another surge strip, etc... everything I saw in various forums.
*WHAT FINALLY WORKED FOR ME:* I unseated the video card, blew off the connectors with compressed air and reinstalled it. At the same time, I pulled the second drive I had installed in the tower (original drive is 250GB and I had put in a second 80GB drive). Rebooted the system and the monitor started up just fine.
I'm skeptical that this issue lies only with the monitor's power supply. After spending 6 hours trying to resolve the problem, I question the following as possible culprits:
1. Could our computers be drawing the necessary power away from the monitor? In my case, pulling that extra drive could have been the solution.
2. Could our connectors just be dusty? I've noticed a lot of posts around this issue are running big machines... towers and Pros. These generally run hotter and keep their fans moving... creating more dust. In my case, both my other machines that the monitor connected fine to are very clean inside. My MacBook Pro is new so of course it's clean. But my mini is older than my tower, and is still perfectly clean inside... likely due to the fact that I barely use it. But my G5 tower that had the monitor problem is my workhorse... the fan is constantly running. When I opened it up I was shocked at how filthy it was. Martha Stewart would have gasped at the sight. Perhaps the connectors on these monitors are extra sensitive?
3. Could the issue lie in VRAM? In my case, pulling the video card and reseating it would have cleared the VRAM, yes?
These are just thoughts I'm throwing into the mix for consideration, based on what worked for me. I'm just glad to have it working again. Apple should be of more help with this issue... their support documentation on this is terrible... reflects the fact that they have no clue what the problems are and/or they don't care to dive down into something so complicated in order to help us.
*I buy Apple so that these things won't happen.*
Apple, we shouldn't have to hold torches to our computer equipment and flit about in voodoo power strip dances to get our expensive machines to work.