Check the battery on the G3. Should be 3.x volts.
The video card for the G4 is probably an AGP, you need a PCI for the G3. See the pic below.
Does the monitor blink or click or do anything doing startup other than no VGA message?
To test the G3, boot it up, give it enough time to finish. Alternate hitting Command-Period and then the Return key a few times to dismiss any dialogs that may have come up that you can't see. Next either push the power button on the keyboard, or hold Control and hit the Eject key and release. You should hear the computer Bonk or whatever, then hit Return. If the computer shuts down it is successfully booting up and it's probably just the video card. Those key combos bring up the shutdown dialog, try it on the working G4 to see what it does.
Yes, I'll be here till the lights go out.