Hello again! Thanks for the info and the upgrade note. That all makes sense now. 😀
I looked at the specs of the Apple Displays to see if there is a callout for either system compatibility or video card requirements. The specs for the current 20" model do not address any desktop Mac older than a G5 so it's hard to tell if it will work on an older G4 at all. The MacTracker database, a third-party app that lists specs for all Apple products, says of the current 20" display:
Mac with any NVIDIA or ATI Radeon 7500 (or better) graphics card and Mac OS X v10.2.8 or later. Windows PC with DVI ports that support full single link digital bandwidth.
but that cannot be considered "official," although I've not found errors in it for Apple products I have used. Still, your video card does not qualify as
"any NVIDIA or ATI Radeon 7500 (or better)" so you would need a newer card with a DVI video-out port.
I can find only one new retail card advertised as being 2X compatible, here:
http://eshop.macsales.com/item/ATI%20Technologies/100435068OB/
The "gotcha" is that it needs a 300W power supply in the computer and the G4 AGP graphics is listed as having only a 200W unit. Upgrading the computer's power supply is not a feasible option. That leaves you at the mercy of the used/pulled card market where there are a lot of pitfalls.
You could consider a third-party flat-panel monitor; they are cheaper and many have both VGA and DVI connectivity that might work with your existing card, although your will have some limitations on desktop resolution and color depth. I don't know if your existing card will support widescreen resolutions, however.
You might want to repeat the question in the forum for older G4s
here. You are in the forum for the latest generation G4s that have 4X AGP slots and came with DVI connectors on their video cards. Maybe someone in the the other forum has worked out a solution on a machine like yours.