Freecom external drive USB plug broken -- how to recover data??

The mini USB plug on my Freecom external hard drive has come loose and broken off, rendering the thing useless. I opened the case and can see exactly what the problem is... the little pins from the plug itself are not making sufficient contact with the circuit board.

If I hold the plug and press tightly towards the circuit board, the hard drive gets powered on (or at least the LED turns on), but it doesn't seem to be sufficient for Windows to recognize the drive.

I'm wondering if I should take the thing apart some more, remove the drive from the circuit board, and try connecting the hard drive to my computer directly using a hard drive cable... What do you think?

Alternatively, could I purchase a replacement enclosure and "transplant" my disk-drive into the new enclosure? If so, where could I buy something like that?

Please help.. I am freaking out here! :banghead