You can't use the iMac G4 as an external display from the mini, or any other computer, without modifying the internal connection to the display panel. It's not a project for the occasional hobbyist, however.
But, there's another way around that...
Connect your mini to the iMac with a Firewire cable.
Boot the mini to target disk mode (press and release the power button, then hold down the T key. After a few seconds, you will see a floating firewire icon on the mini's display. You don't need to have a display connected - so just holding the T will get there, even with no display attached.
Now, restart your iMac, while holding the Option/alt key on the iMac's keyboard.
You can choose the mini's hard drive to boot your iMac. And, now the iMac is using the mini's hard drive as the boot drive, same as it would with any external hard drive. You just have to remember to boot the mini in target disk mode each time you need to boot up.