I have a black screen on my Duo. Wen I press the power button to turn on, the second light which indicates that it's starting up, blinks once and nothing happens. I'm out of warranty and am attempting to repair on my own. I've tried the simultaneous fn/power button exercise, to no avail.
Do the lights stay on? Hard-drive spins up? Could be a bunch of things, if the lights stay on and the computer seems like it's booting, attach and external monitor to it, your screen could be dead.
If the lights don't stay on or no fans go on, drive is silent, could be battery, charger, motherboard, ram, cpu. I'd start with booting with no battery. If that fails, try a new charger, then try new ram. Once you get past that and get nothing, you should probably look into a new laptop as a motherboard replacement would cost almost as much as a new system.