HELP: No video and fast flashing green LED

I have a Dimension 4100 with a P790 Monitor. The monitor worked fine last time it was in use but now will not show any picture. I have completed all the self-tests I can, based upon the support on this site, with the following results:

1. The PC boots normally with a single "beep" at POST.

2. The monitor does not show any self-test check screen (or any other) when started connected to a clean power source, but not connected to any PC. There is just a blank screen as though the monitor were off, but the single green LED on the front flashes rapidly.

3. The monitor does not show any self-test check screen (or any other) when started connected to a second, known to be working, PC. As above, there is just a blank screen as though the monitor were off, but the single green LED on the front flashes rapidly.

4. I have seen posts that refer to reseting factory settings by pushing combinations of the controls simultaineously. This has no effect.

Th