Power Mac G4 Cube not booting
Got an copy of DiskWarrior? (DiskWarrior usually fixes this issue for me) 

Have you tried "Safe Boot" ?

What 10.3 and 10.4 install CD's are you using? Are they for the Cube? Another Machine? Generic installers? 

May try booting to an external drive, and running the 10.3.9 or 10.4.11 combo updaters on the boot volume.