Tony,
It does sound like a serious problem with the logic board, probably the VideoRAM and/or ATI graphics card. The internal display has a data cable, inverter cable, and inverter that connect to the logic board; even if the display's LCD or fluorescent bulb or any of the aforementioned items was bad, the video output to the external monitor would not be affected. Since both the internal and external display go "wonkers" at the same time, this would suggest the logic board.
One item that can affect video output to any source is a poorly seated microprocessor card, although your symptoms are not exactly the same. If you wanted to cover all bases, reseat the card:
Remove main battery, power adapter, and optical drive; lift off but do not disconnect the keyboard; lift off the heat shield; remove the top memory module. Now press down very hard on the right side of the microprocessor card next to the HD and closest to the palm rest. Without reassembly, connect just the power adapter and start up and test. If no success, press down even harder, then test again.
I don't know if bad RAM can also cause an issue like this. If removing the top memory module makes no difference, you could lift out the microprocessor card, replace the bottom RAM module with the one from the top slot (and leave the top slot empty), then test.
Here is Apple's guide to replacing memory in the top and bottom slots:
http://docs.info.apple.com/article.html?artnum=50028
Here is iFixit's guide:
http://www.ifixit.com/Guide/Mac/PowerBook-G3-Pismo/6/