you can check the external hard disk condition with HDDScan
. Just click on "S.M.A.R.T" and see what's green and what's not. Also, do you hear 'clicks' from the hard disk?
Otherwise, you have to dissect the hard disk from the external enclosure and put it into your PC and test if it works there, just like what brandonwh64 said. If it works, you can then make backups of the important data that are in that hard disk.
But if there's no important or super private stuff in the external hard disk and you still have warranty, then perhaps just rma it and get a replacement.