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?

Specifically this is a:
Hitachi Travelstar 4K120
2.5 inch ATA/IDE hard disk drive

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!

I don't see any reason why connecting it directly wouldn't work . You could pick up a 2.5" > 3.5" IDE cable and connect it to your PC (if you still have IDE slots onboard), or go for a usb caddy enclosure and turn it back in to a portable drive.

Personally, I'd go for the caddy as it costs only a little more and still gives you full intended use of the drive. Here's a link to some of the products available.