I'm assuming you are dealing with a titanium PowerBook G4 here. There are 3 cables that connect to the logic board from the display module. There is a 2-pin LED sleep cable (white and blue), a LVDS cable (extremely thin wires, multicolored), and on the other side is the inverter cable (heavy gauge, white and pink).
The inverter cable carries the high voltage needed for the backlights. It connects to an inverter board which ultimately controls the brightness of the display. Be extremely careful when working with the LVDS cable, I can't stress this enough, they are very fragile, I don't believe that cable can be replaced separately like it can on the iBook (which is a pain, but cheaper than the whole display).
I would start by eliminating any software problem by booting into a different OS or user, and even try an archive & install (or clean install for 9). Try zapping your PRAM by holding Apple-option-p-r at startup until it boings twice. Try your Apple Hardware Test CD, as it sometimes picks up helpful (usually expensive) errors. Only then would I take everything back apart and make sure all cables are securely seated or pushed in. If it still continues, i would bet that the inverter board has gone bad for whatever reason. Try some of the first couple steps and see what that does.
However, I was unaware that the hinges on theses models were replaceable, I've never had to do that. Depending on what is involved in getting that far into the display, you may have bumped something internal to the display. If you do have to go that far again, don't put any pressure on the back of the LCD, so you could end up with white spots on the screen.
I replaced the hinges on my Lombard PowerBook a while ago, and recently noticed that my backlights would shimmer, and sometimes go off completely. I took it apart and tightened everything up and routed the wires better and is working flawlessly now. Luckily something just came loose! Good luck!