The video out connectors on a desktop Power Mac G4 are VGA/DVI/ADC
So that display will probably have a VGA connector input. (VGA = D-Sub)
So if you order a Mini Display Port to VGA adapter with your mac mini, it should work.
If your monitor has a DVI input, then rather buy a Mini Display Port to DVI (Digital signal), VGA is analog.
If ADC is the only connection available on your display, then you would need a DVI>ADC adapter. (MDP to DVI is included in the box of a new mac mini, so that would be MDP>DVI adapter to DVI>ADC adapter to Display)
- not available anymore in stores. Maybe 2nd hand ?
- new price was 99$
- not elegant: the brick provides the power for your display.
(Your G4 video card with ADC output, provides power to your screen, through the ADC cable.)
It is possible you run into problems, two adapters to convert video signal is not ideal...
If I were you, I'd buy a new display (or second hand) with HDMI or DVI input.
LCD displays don't cost a fortune anymore, and provide decent quality for the average user.
LED displays are more expensive, buy this only if you really know why.
HDMI cable: a cheaper cable will do. A cable of 60$ doesn't give you better quality then a 15$ cable. In the digital domain you have either a perfect signal or no signal at all. If you want I can explain more.
If you have one of Apple's wonderful Apple Displays you are out of luck - it uses the ADC port which is no longer supported. If your display has a DVI-D cable (it has two sets of 3x3 pins and a long narrow prong) the mini ships with a connector that supports it. If your display's cable has 3 rows of 5 pins it is VGA and will require a mini-display to VDA adaptor.
Many many thanks for the very detailed reply. I know exactly what options I have available now. Secondhand adapters are on eBay but seem to go for a fair bit. I think you are right and maybe time to upgrade ;-)
dwb...your input was also very much appreciated. It is indeed the Studio Display.
Might be simpler just to put a big cardboard box over the G4 to keep the noise down!
I'd forgotten about this monstrosity. Seeing the price I remember why my wife gave me the Studio Display for my G4 tower when she bought a new MacPro at the office. For about $100 more she got a brand new display that was larger than the 17" ASD. Who knew that monitor would still be going strong (and look good compared to newer displays) 12 years later! My G4 tower is now in use as a backup server where I work and I'm still using the ASD.