What could be broken?

Your power appears to be fine. Try starting up from your installation disk. Insert the disk part way, hit the start button and push the CD all the way in. Immediately hold down the "C" key and see if it will boot. Next do the same thing with an external monitor plugged in.

My 12" PB got dropped from about 5 feet by a porter and then failed to come on. When I pushed the 'on' button, I'd hear a couple of clicks, feel the HD spin up but nothing else. No screen, non-responsive to keys and had to not only unplug it, had to remove the battery to turn off. The top of the unit where the HD sits got EXTREMELY hot. Was told by a 'repair' shop that the motherboard was damaged and it would be cheaper to get a newer machine than repair the PB. That was 15 months ago. A couple of weeks ago I salvaged parts (memory and optical) to upgrade an iBook and put the old parts back in the PB for practice/experience. I thought what the heck, wonder if it now works?? And it did!! Must have been a connection that got knocked loose. Not saying if your situation is the same but the optical removal was nearly a complete teardown so most if not all the connections were 'broken' and then remade. Couldn't hurt to try on yours. If it does not work, what have you got to lose other than time. Think of the experience you will gain. The instructions provide here are excellent, and easy to follow. Just read them a couple times before starting work (I know, we don't need no stinkin' instructions. wrong). It will make the work easier plus you will catch some facts (like the need for thermal paste for when the heat sink gets re-installed). Just my nickel input.

Try pushing the button on the bottom of your batter and see if any of the lights come on the battery.....if they do then you have some life in your battery and odds are the problem is your logic board.