how does back up work? if i withdrew from 1 of them, would all of them show the change? is it safe to just keep on online exchanges like mtgox and bitstamp? if no, how would i back those up?
Yes, if you store your wallet.dat in multiple places, when you spend the coins on one, the others' balance changes as well.
Yes, it is possible to restore it if you can get to the file.
However the question whether You can do it is hard to answer. Misguided retrieval efforts can, in the worst case, cause further data loss.
If I had ~14k riding on a broken HDD I'd be very, very careful with homemade solutions. As gec pointed out, your best bet is to seek professional help, even if it costs you. That's certainly what I would do in your situation.
by very careful, is replacing the pcb safe?
If you're worried,
seek professional help.