Try "zapping" the PRAM, this will force the video card to query the connected display and you should see an image.
Hold down the keys command+option+P+R at startup until you hear the Mac chime at least twice before you let go; if you don't hear chimes, watch the VGA monitor's indicator lamp which should show active when it first detects a signal, then inactive as it begins or fails to synch, let it cycle a few times.
Clearing the PRAM is a good precaution anytime you are tinkering with hardware, as it forces the Mac to forget what it thought it knew about itself.
If a PRAM zap doesn't help, connect a different display - I have had this problem mostly on really cheap or very old displays that are not properly following VGA standards.
As a last resort, if you are a veteran Mac user you may have some video adapters to connect VGA equipment with older Macs & Apple displays: try putting a VGA-to-Mac adapter in series with a Mac-to-VGA adapter.
(And if you think only Apple gear has this issue, then you never tried to fix a video synch problem in Windows - why do you think Safe Mode is 640x480?)
Take a closer look at your MDD G4: in addition to the 2-drive bay mounted vertically at the rear of the chassis, it has a second 2-drive bay below the 2-drive optical bay, the bay has a second drive sled which goes in perpendicular to the optical drives, and has a 2-head power cable waiting for you. You can even sneak a hard drive into a free optical bay, though you may have to be creative mounting it in place. I have a client whose MDD has been populated with 5 hard drives and an optical drive since new, it has run stably & well within temp.
This Old PowerMac
Building a PowerMac Media Center Part 1: Selecting Your PowerMac