First try repairing permissions on the powerbook. It probably won't help but you can try.
If you just copied the OS from the mini to the powerbook, it won't be the right one since notebooks have all sorts of stuff that desktops don't. It will also miss some things. There are hidden files as well as stuff in both the computer Library and the user Library. Also, if the os on the mini is updated and the powerbook is behind, you'll get conflicts. You need something like Carbon Copy Cloner, or another transfer app. I do not know if it's possible to install on one machine from another using target disk mode, but you can try.
Try inserting the dvd/cd for the powerbook in the mini. Then see if you can reach the powerbook hd when you get the "select disk to install on" window. If yes, If you can try running disk utility from the powerbook cd/dvd and see what it says. If the powerbook cd/dvd has it, you can also run Hardware Test and see what you get. For instance I recently had a RAM module crap out on an Imac G5. When I could not reinstall ISx on that machine, Hardware Test told me about the memory problem.
If everything says OK, you can try reinstalling the original OS. Click the Option button and pick either Archive and Install or Erase and install. The second would probably be best as it gives you a fresh everything - but you lose all your files. If you wipe, make sure you select Mac extended as the format for the drive.
Another thing you can try. I don't know how easy or hard it is for you to get to the ram on the Powerbook. If you can get to it and you have more than one module, try removing one and see if the powerbook boots. If no, remove the other module and reinsert the one you removed earlier and try again. Since it's a G4, I don't thing matched pairs matter. They don't on our Powermac g4s.
Using OSX 10.3.9 & 10.4.11 on a G4, G5 & Intel Macbook