You can either perform a diagnostic test on the hard drive or assume that it's failed and just replace it.
If you want confirmation before replacing it, test it with
Diagnostic Software for DOS which is available from the drive manufacturer's websites. The links are here:
http://www.tacktech.com/display.cfm?ttid=287
Create a CD from the diagnostic ISO file with
IMGBurn from here: http://www.filehippo.com/download_imgburn/
Boot your faulty PC or laptop from that CD and the diagnostic software will open.
Select your computer's hard drive and run the Long/Extended test on it.