Backlight dies, it's not the inverter or LCD

I'm troubleshooting a 12" iBook 1.33 Ghz. Boots up normally but LCD backlight dies after boot process ends. It also goes to hibernate repeatedly after a few seconds but can be awakened by pressing the space bar. I've replaced both the inverter and LCD panel but no joy. If I hold <option> key after the welcome chime sounds, the screen goes to display the hdd icon as the only bootable OS X, and the backlight does not go out, even after waiting 30 minutes if I just let it be. The arrow cursor works before the hdd icon comes up but it's very sluggish and moves very slowly. After the hdd icon comes up, the cursor moves normally.

Is it possibly the software or bad hdd, or bad logicboard?

It's a 12 inch iBook, Model A1133, 1.33 GHz. I can't verify the serial number by software because the screen darkens before I can call it up, and there's no info in the battery compartment like the powerbooks.