Thanks for helping me with this.
Yes, the DVI port.
If I plug in my older 15" ADC monitor (ie. by itself) it seems to work. That is, it hasn't exhibited the symptom of the DVI port yet. However, if I hot plug the ADC monitor in while the DVI monitor is plugged in and experiencing the "not turning on" symptom, the ADC remains black. If I startup with both plugged in, the ADC will turn on while the DVI will misbehave. When this happens, the system thinks the DVI is on (as the main monitor).
more data:
The DVI monitor is a Viewsonic VX924 19".
If I cycle power on the DVI monitor during the symptom, it will flash the "no signal" message. If I turn the DVI monitor off (or switch to the analog input) at any time, the workaround is required to get it back on.
The reason I am suspicious of another cause outside of the video card (warranted or not) is that this is exactly the symptom of my old card (also Radeon 9000). I assumed the problem was the card and replaced it with another used (yes, a possible red flag) 9000. It fired up the first time after installing it but now a week later is back to it's old tricks.
Do these Radeon 9000 cards have a history of this?
Could there be something up with the monitor that's beating up on the card?
I'm using a 10' DVI cable. Again, the cable and monitor work with both laptops.