There is probably a mark on the disk...
My Cube has a slot loading DVD drive. Nearly every time I tried to insert my copy of the Lacie 161040A CD-RW software CD, I would hear the drive make a constant angry-5-year-old noise at about 600Hz vibration sound for about 5 seconds, then eject. In order to circumvent the issue, I shoved the CD into the drive with the palm of my hand, but not so much as to act onto the CD like stepping on it, just enough to get the drive's attention...and the CD worked almost every time with this alternative method. Probably the extra shove caused the disc suspender (or whatever the mechanical term is) to skip a step or two in reading the CD, which worked.
Now I'm not sure if you have a G4 with a solt-loading drive or a tray loading drive. If you have a slot-loading drive, the process I described above should work with approximately the same success rate I had with my marked disc. Otherwise, if you have a G4 with a tray drive, the slam-the-tray procedure might not be as direct as inserting the CD into the CD repositional devices and altogether might not circumvent the issue.
Watch out for specificallly that disc in the future when you need it again...you're going to have hell with it if you forget why it loaded before.