Buy an external hard drive enclosure like this one [link to www.newegg.com] , get the laptop drive out (shouldn't need to do more than to remove some screws at the bottom to open the drive bay) and pop it in the enclosure, connect to another computer and you can recover the data.

Getting the laptop power port fixed will either require some soldering or a whole new motherboard (depending on the damage done), which won't be cheap.