Do you have the HDD back?

You could try sealing it in a freezer bag and leaving it in the freezer for 24 hours. There's a slim chance this might get you 15 mins to a couple of hours worth of operation in which to copy across as much data as you can.

There are reports on the web of the freezer trick working, and if it's not going to cost anything then it's worth a try.

The alternative, as others have suggested, is the platter swap. Either set up a donation fund to pay a professional recovery firm to do it, or risk attempting it yourself. What's the make/model of the drive, and have you checked how much identical drives go for on eBay?