Two VGA monitors don't work with two different G4s, but both work with G3!

Question

I recently acquired two used Power Mac G4s (one of them is a mirrored-door dual-processor that I got from school and was told should work, the other is a Gigabit Ethernet model, and should also work), from two completely different sources. They both turn on (I get a power-on light, I hear HDDs churning, and I get a power chime from one of them, and they react to the usual Mac stimuli, mouse and keyboard light up, reset button works, etc.) but I get *absolutely no video*. The monitor syncs for a second, like it gets a quick signal, then goes immediately back to the "CHECK SIGNAL CABLE" message.
I have tried them both with two generic PC VGA monitors (though they were both kind of old and crummy ones, they work on my G3 and other computers. I've tried the working PCI video card from my G3, that doesn't work, nor does swapping their video cards. They both have Apple-supplied ATI AGP video cards, both with Apple's proprietary ADC interface, though one has only DVI out (with a DVI to VGA adapter that came with it) and the other has a straight VGA port.
The weird thing is that, even though these computers have never, er, met before, they have the exact same problem. The only thing these things have in common is the monitor I'm using. This leads me to believe
The only thing left I can think of is to hook them straight from the DVI port to my HDTV, but I don't have a DVI cable, much less know ANYTHING about DVI. Could it be that these particular VGA monitors don't like AGP video cards, or some sort of weird incompatibility that isn't well known?
I figure if anyone's seen something like this, you guys have. Here are the AppleHistory entries on these machines, if it helps:
http://apple-history.com/body.php?page=gallery&model=g4giga&performa=off&sort=da te&order=ASC
http://apple-history.com/body.php?page=gallery&model=g4_mirror&performa=off&sort =date&order=ASC

Answer 1

The software on the hard drives may be set for a video setting that won't work with your monitor. A few things to try (in order):
1) Reset PRAM. Hold down Cmd-Option-P-R when booting until you hear the third Boing.
2) Hold down Option when booting. Should show symbol of hard drive, plus a couple of arrows.
3) Boot from a CD (Install disk or, preferably, Hardware Test Disk).
4) Safe boot. Hold down "S" just after the boing. Release it when (if?) you see the turning gear.
If it is a scan rate problem, one of these should show some video.