Is the optical drive in the Mac Mini confirmed to work?
As great as the little Mac Minis are, I feel their weak point is the optical drive. I found they fail more than any other component. I hope yours will not! (by the way, sounds like the same problem with your iMac G5 drive not reading the Tiger disc ... the drive on my 2005 iMac G5 failed after only 5 years and the Apple repair guy was like "oh, yet another one dead ..." ).
If you're not looking for speed, you should be able to just get along with an external USB 2.0 drive connected to the iMac G5 / Mac Mini G4. I've got one as a backup, though rarely use it ever since switching to a firewire one.
But those are usually really cheap to have as new. Depending on where in France you live, the d'Arty or Pulsat near you may have some in stock for about 20 to 30 euros each.
Come join us on Hotline when you got your Mac Mini G5 all set up 
personally i removed the drive to make space for heat management and im using an external one within my mac mini stack
The issue with my iMac G5 was how to install DVD macOS Tiger. Did not managed from usb, either from FW 400 HD or recent external usb Drive.
Maybe a HD issue + Combo issue ?
When using the Alt key on booting, only the HD was recognized.
That's why I just bought the Mac mini.
First of all, few days ago I planned to install Mac OS 9. I boot my Power Mac G5 and after few hours, I heard a "firecracker" and the computer turned off. I disassembled it to remove the power supply, which I also disassembled. There was a lot of dust inside. Then I performed the PS ON test on pin 14 with a paper clip : the fan did not start. I found a broken piece of electronic component inside with a part of the numbers, but I couldn't determine where it came from after closely examining the motherboard and the power supply. Was it sucked in at some point in the past and has been there for a long time ?
I then traded a Dell tower from 2005 for the iMac G5 that we're talking about.
Never give up....