Since your HDD is from Seagate, download and use their Seatools utility for thorough tests and tools. Find out about it here:
http://origin-www.seagate.com/support/downloads/seatools/
Personally, I prefer the "for DOS" version. You must download an .iso file and then use your own CD-burning utility (like Nero) capable of burning this .iso image to a CD to make a bootable optical disk. You then boot and run from this disk to use their menu-driven set of utilities. You do NOT need any functioning HDD in your system to use this tool.
However, in your case you do have a functioning system with a bootable HDD and Windows working. So you can download instead their "for Windows" version and install it on your C: drive. Then you run it as a Windows app to work on your troubled HDD. On that page linked above, there are links to download the .pdf files of instructions for each version of Seatools. Check them out.
There are two tools you may need for your situation. In the "for Windows" version under Section 3 : Advanced Tests and Features, you'll find "USB Erase Boot Tracks" which says it will work on a HDD in a USB enclosure (I'm presuming that is what you have now) to wipe clean all the key data at the start of the drive so it can be "seen" as completely empty, and should function just like a new empty HDD. That might solve your immediate problem. (I don't know whether the "for DOS" version has this same tool.) The next tool is "Full Erase (SATA)" which does what I outlined in my post above dated June 25 - a Zero Fill that also forces a diagnostic to replace faulty Sectors.
Be CAREFUL of these! Each of these tools is completely destructive of data on a HDD - you cannot recover any data after using them! Now, for your use on the troubled old HDD, that is not a problem - it is actually what you want. BUT you MUST be very sure that you use the tool ONLY on the bad HDD, and NOT on your boot drive, or any other good HDD in your system.