I would wager to say the motherboard may be the least of the worries. I would suggest trying to remove the hard drive to be backed up to another computer and get something new.
Normally, I'm not a fan of tossing out the whole thing, but if that sucker's been dropped than many times, between the motherboard and/or display, things could become expensive quickly. Unfortunately, unlike desktops, there's not a standard form factor for laptop motherboards, so they tend to run higher for that reason. If you're adventurous, you could see if a computer shop would diagnose it for you and then get parts from eBay and fix it yourself. Otherwise, if this goes beyond one thing, it's probably not worth it.
