Update 2012-03-19: I never figured out what the problem was because the screen started to work again after reinstalling OS X 10.6 for a second time. I sold the Mac on eBay a few months afterward (I explained the full history ;).
Original Post: My Late-2008 Aluminum MacBook Unibody screen doesn't usually turn on. External displays work via the Mini-DisplayPort.
Sometimes when power is not connected, the lid is open, and I have the external display connected, the internal monitor will work! When it works, it stays on until reboot.
- http://support.apple.com/kb/ht3964 (SMC Reset)
- http://support.apple.com/kb/ht1379 (PRAM and NVRAM Reset)
I've been told by an independent, authorized Mac repair company that the logic board needs to be replaced. That seems a bit excessive to me, although I've read many similar diagnoses online.
Any other ideas?