Broken PowerBook G4

My PowerBook G4 is broken and has been for a couple of months now. I owned it while it was working for about 1 and a half years. When it broke originally, I was restarting it after changing the boot logo in the system files and when it rebooted, it just stopped at the bright blue screen that I'm pretty sure comes right before the grey apple logo on a grey background. I left it for a while and it never finished booting. So I restarted it again and the same thing happened several times. I then opened up the RAM removal door and saw that there appeared to be slight decay to one of the sticks of RAM. This may or may not be a problem. I removed the RAM and started it and the computer beeps as it should when it doesn't find the RAM when I put the RAM back in, the computer makes the chiming noise, but the screen does not turn on anymore. (By this I do mean that no part of the screen is lit. No backlighting occurs and pixels remain dead.) This is strange because before I removed the RAM, the screen turned on but stopped at the blue screen. I also attempted hooking the computer up to another Mac via FireWire and repairing the hard drive. I then got a USB and put Leopard on it. I cannot boot from the USB either. I have tried all of the obvious including resetting PRAM and resetting PMU. Neither of these had any effect on the computer at all. I even tried removing the main battery and letting the backup battery charge over night snd that also had no effect on the starting of the computer. I also tried hooking it up to a Mac display and that did not work either. That test may be unreliable, however, as I have not confirmed that the display itself works as I do not have the appropriate cables. I am now at a point where I have the computer where it boots up, chimes, but the screen never turns on. I have the Leopard install image on a USB drive, and the hard drive is repaired. (Disk Utility said that it was corrupt and I repeaired it in Disk Utility as well.) I do not need the files that were previously stored on this computer. It previously ran OSX Leopard. Any other ideas on what I could try or what could be going wrong here? I have previously thought about it being a Logic Board issue and this seems to be agreed by first answer I got. Are there any steps I can take to isolate whether or not it is the logic board? Is there any easy way to fix or replace it?