Shine flashlight into the front of LCD. If an image is being displayed. GPU (Nvidia) is fine cause image is present but backlight is not ON. Check logic board connections. You also said external display works fine via mini-DVI port. So Logic board and Nvidia is fine. Reseat and check that the display connections to the logic board are secure. If it is still the same I would suspect display assembly. If still the same after display then poor or no backlight LED Driver power, faulty logic board.

I would suspect cables connectors.

Connect external display, clear PRAM to set brightness to default level and verify. Verify display listed in the System Profiler’s Graphics/Displays device tree is not disappearing intermittently (refresh System profiler to observe). Inspect and reseat the LVDS cable and camera cable connection between display and logic board. Also test if brightness setting is a contributing factor. Has flickering stopped? Swap RAM with known good RAM to determine if video issue is RAM related..

MagSafe LED ON, indicates power flowing to logic board. So: Reseat the keyboard flex cable to logic board. A disconnected keyboard or a stuck/open power-on key can disable system powering on. If power button does not work, use jeweler’s flatblade screwdriver to short the Power On pads on logic board to power up the logic board. If power-on key is stuck, keyboard flex cable might need to be disconnected before shorting pads. Verify that system powers on. Replace top case for stuck power-on key. If shorting does not help, Remove logic board and verify that the MagSafe connector is correctly connected underneath logic board and Reseat MagSafe connector on logic board and retest.

Verify AC power presence with MagSafe LED indicating on, or in charge state. Try booting unit only with AC adapter and with out the battery. Inspect unit’s AC adapter and verify that cable and MagSafe connector have no damage. Reset SMC. Reseat battery connector and retest. If physical damages are found, replace damaged parts and retest. Unit’s battery may be run down, or not recognized. Substitute unit’s battery with a known-good one to verify that system starts on battery. Else the issue may be with the Logic Board.