It depends on what the problem is. Did the hard drive itself become damaged? If the computer works but the hard-drive doesn't then putting it in an external enclosure wouldn't help. If you take it in to a computer place there's a chance they might be able to recover some of it.
If you REALLY need the data and they can't recover it you can spend $600-800 at a data recovery place getting them to read the individual platters in a cleanroom. That will get you the most data back but is quite expensive.