Why won't this g4 PowerBook boot up properly?

I've recently replaced the lcd screen on a g4 powerbook that a friend gave me after she'd dropped it onto a cement floor which damaged the lcd screen. I did the screen replacement myself which, for all intents and purposes went well but now I'm having a boot problem with the computer.

If I shut it down and it's been off for any length of time (overnight), when I try to start it up again I can hear the hdd starting and the boot chime sounds but then the screen remains black. I then go through the keyboard commands that I've read about to try and get it to start properly, such as, Option-Command-Esc followed by Ctrl-Command-Power button followed by holding the Power button down for 10 seconds but then when I try to boot it up again I don't hear the hdd starting and no boot chime.

I'll go through these steps a few times with no luck but then if I let the laptop sit for a bit and start going through these steps again it will usually restart properly after the 2nd (keyboard restart) step and everything works.

I'd really like to get to the bottom of this odd behavior. Could it be a faulty inverter or is it more likely (heaven forbid) the logic board beginning to fail or (hopefully) none of the above?

I'm currently using the powerbook to ask this question using just battery power in order to see how long the battery lasts, it's gone from 99% to 31% in approximately 45 minutes. I also want to run the battery right down to zero to see if the AC adapter will charge it back up to full capacity.

Any help and/or suggestions that might lead me to solving this dilemma would be most appreciated.