First thing, hot-swapping the drive like that is a sure recipe for disaster. Even if the enclosure is for an external drive, actually opening the enclosure and hot-swapping the drive itself is not proper operation.
To gain access to the files (if the HDD itself is still OK, but the enclosure is toast), you could use an external HDD bay. Google for something like that (the HDD can be plugged in the bay and the bay itself connects to the PC via USB). You can try to access the files from there.
If Windows gives you some access errors, that means the filesystem is corrupted. Do not rush to re-format the drive, you can plug it in a Linux-based PC (like one that runs Ubuntu) and access the files from there. Good luck.