|"Would replacing the hard drive fix the problem?"|
It's impossible to say at this stage so don't spend money on a new one just yet in case it's something else. First you need to test the hard drive to see if it has failed.
You can do that yourself using diagnostic software available free from the drive manufacturer. The links are here: http://www.tacktech.com/display.cfm...
You need to download the DOS version, not the Windows version.
The DOS version is in the form of an ISO file which has to be burned to a CD.
Then boot the faulty PC from that CD and the testing application will appear on screen. Run the "Long Test". If it says "failed", then indeed the drive needs replacing with a new one.
If all that is too much to take in, get someone to help who is computer savvy.
Or you could just buy a new hard drive and hope that's what it needs -- but as I said, you could end up wasting your money if you don't test the existing drive first.