First, I just want to be sure about something: you do NOT want to save ANYTHING from that old HDD, right? Because my suggestion will destroy all its old data and apps.
I think this is what has happened: Windows often protects itself from user mistakes by refusing to Format a Partition or even Delete any Partition from a HDD that is bootable and contains Windows OS. But there are other ways to do this with third-party utilities.
As an additional thought, my preference when preparing to re-use older HDD's is to wipe it completely clean AND force a thorough self-diagnosis of the drive unit. The best way to do this is to Zero-Fill the old HDD. This writes all zeroes to every sector of the drive. Each such write also triggers an internal self-diagnosis process that re-reads the Sector and analyzes the quality of the signal. If the signal is weak in any way, the drive treats that as a warning of future failure. So it retires that Sector, and replaces it from a stock of known-good spares. When it is finished the entire operation (takes hours!) there is NO "Bad Sector" on the HDD that any OS could gain access to and use, so the HDD appears perfect to Windows. This is a normal background process that Windows (or any other OS) does not know about, but it is supposed to happen all the time during normal use. But just in case that has missed something in the past (say, a Sector went bad but nothing tried to read from it later), this Zero-Fill process will force EVERY Sector to be examined as it is wiped clean of old data.
In a linked step, the HDD's on-board SMART system does many things to monitor the unit, including keeping track of how many Sectors have been replaced as suspect. Eventually it hits a limit and sends out a warning that many replacements have been made. This foretells two things: (a) the stock of spare good Sectors is getting low, and this cannot continue forever; and (b) since so many Sectors have been found "bad", the projection is that this will continue to happen at an increasing pace. For both those reasons, THIS is the time to back up your HDD completely and replace it while you still CAN read all its data. So, IF you get a SMART warning of failure in the near future after doing the Zero Fill, just replace the drive. If not, use it in full confidence that it has no significant problems.
Now, how to do that? Check which manufacturer made the drive. There are third-party utility packages you can buy or download for free that will do a Zero Fill. But the handiest source may be your drive's manufacturer's website - the "trick" is, their utilities are specially coded to work mostly on their HDD's and not others. So if your old HDD is from Seagate, download their Seatools diagnostic utility. IF it's from WD, get their Data LifeGuard utility. (Other makers may have similar diagnostic utility suites.) Each of these has many tools to test and fix (in some cases) their HDD units, and include the Zero Fill tool. Each also comes in several forms - a "for DOS" version and a Windows app, for example. Personally, I prefer the "for DOS" versions because they are used as bootable CD's that install their own mini-DOs and let you work with NO functioning HDD in your computer - you do NOT need any OS or working HDD to use this tool, so it can help even in tough situations when your OS cannot deal with the troubled HDD. The "trick" requirement, however, is that the "for DOS" versions actually download as an .iso file. This is just an image of the CD you need to burn yourself. So you need a CD-R disk and writer and a CD burning utility like Nero that can burn the .iso image to the CD-R. Once you have that CD made, you place it in your optical drive. Power on and go immediately into BIOS Setup and set your Boot Priority Sequence. Make the optical drive the first boot device, and the normal C: HDD your second one. SAVE and EXIT and the machine will boot from the CD. It will load its own mini-DOS and ask you to specify which HDD unit you want to work on. Make sure you get that right! It will show you some info on the HDD, including a readout of the SMART data it has. Then you get a menu of tests and tools to use on that unit. Many of the regular tests do NOT destroy any data. BUT some tools do, and they will warn you of that and require confirmation that you do wish to proceed. In your case, the Zero Fill tool will be like that - it DOES destroy all the old stuff on the HDD so you must confirm. Then wait patiently. When it's done, check the new SMART info to ensure there are no important warnings.
There is no simple exit from this utility. You should remove the CD from your optical drive and reboot - it will boot normally with no CD in the optical drive. Now you can go into Disk Management to find the old HDD completely empty like a new unit. RIGHT-click on its Unallocated Space and choose to Create a New Simple Volume (Win 7 or 8), or Initialize (later versions of XP, etc.). You can specify the size of the Partition (I assume you'll want to make one Partition that uses the entire HDD). You probably should make this NOT bootable, since it is to be used only for data (no OS installed on it). For Formatting options, use the NTFS File System (default) but you don't need to do a Full Format. Full tests every Sector and takes a long time, but you just did that with the Zero Fill operation. Just use a Quick Format.