Very unlikely. Given you have no 5v or 3.3v (and I guess no 1.2v or 1v either) there's no power getting to any of the switching regulators. The most likely culprit is a shorted capacitor on the input side since only the 2250 is getting hot. Normally a failed MOSFET doesn't get very hot as either it's a dead short or it's gone open circuit. I'm guessing the 2250 is some form of input side switch controlling the charging but TBH it could equally be a switching controller, though the 7401 is the more likely candidate for that. Without datasheets or looking more closely at the board and tracing some connections it's hard to say exactly.You think one of the inductors could be an issue?
More than likely.No it does not. The problem is that the laptop does not switch on at all. With regards to running on battery power, it could just be that the battery is dead.