If you're referring to the 23" Apple Cinema (LCD) Display, it requires a DVI output on the graphics card. The ATI Rage 128 Pro card that shipped in some G4 DA models has VGA and ADC ports. You'll need to upgrade to a graphics card having a DVI port and one that's capable of supporting the Cinema Display's 1920x1200 @ 60Hz native resolution.
Why take a Seurat painting, smear it up some to make it look like a da Vinci? Japamac is right. Digital is digital and analog is analog. Don't try to fit a square peg in a round hole even though you can round the corners to do so.
A DVI to VGA just extracts the Analog signals (from that cross-bar thing at the end of the connector and the pins around it). It doesn't convert anything, and it doesn't work the other direction.
You would need a VGA to DVI converter (over US$300) which has all the VRAM and logic of a Display card. Much simpler just to get a fast enough display card with enough VRAM to do the job in the first place.
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ATI Rage 128 Pro
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