This may be stating the obvious but often it isn't the HD that has packed up.
I have just had a PC die on me, with "classical" HD failure symptoms. In fact it was a duff motherboard. I bought another (exact same type) MB on Ebay, a new power supply (on Ebay too) for good measure, and replaced the MB and the PSU. Everything is now perfect.
HD data recovery firms are very expensive; a few hundred quid upwards.
A proper backup solution is the only way. I use a DDS4 tape drive; the tapes hold about 13GB each.