run
chkdsk /f /r windows will try fixing whatever wrong.
chkdsk runs when your system is booting.
Windows gets hung does it happen without the External connecting to the system.
Run virus scan. How do you think you can format your external without removing your data from the external.
If your system gets hung only when
Link with Steps for daarecovery
If your system gets hung on adding he external, then first run chkdsk, then add the external and then reboot. See for the results. Look up the link I have given you they are the best steps you can follow on your own for such a case.
If it is gone foreever for real you cannot help, get it replaced. Except the chkdsk will help you to recover few data, after clearing of inconsistencies in the HDD.