I have the same problem on my Power Mac G5 2.5 ghz DP Quad.
I have changed the video card, not the video card. That has been tested.
When I power on the computer always chimes.
When I have no hard drive cables plugged in I get video, 99%.
Sometimes I have to reset the Power Management, unplug, press reset, remove battery, power on, turn off
then insert battery and power on again.
I am thinking maybe the cables.
The worse scenario would be to have to replace the processor or the logic board.
One successful time with the hard drive plugged in I got video for about 5 min.
Then the video went away. I am going to test all the cables first.
I am beginning to think the processor.