There is a good chance the problem is the enclosure, not the actual drive. You might be able to open the enclosure and remove the drive, then install the drive in another enclosure, or into your PC as a secondary drive (NOT boot drive), and copy, or continue to use the drive from there.
The only issue becomes the connections on the actual drive used in the enclosure. Many enclosures use standard EIDE or SATA drives and will not be a problem. But sadly some external drive makers permanently attach proprietary interfaces to the drives that directly support the USB interface and may not easily be used as an internal drive. They may allow you to use an adapter, but may not. The only way to tell is to open the enclosure and have a look at the back of the drive.