Get yourself a HDD docking station, extract the HDD from it's enclosure, insert it in the docking station, plug that in your PC and see what happens. If the HDD was formatted in FAT or NTFS, it should pop-up like an external drive and the PC should give you the option to open it. If it was formatted in some ext3 or ext4 filesystem (and the enclosure controller would handle the disk administration), you can do the same by using a linux-based machine (or a Mac, I guess, but not sure there) to mount it. Either way, you will be able to recover your files.