The problem with that is you want to keep the programs and Microsoft has been making this progressively more difficult with every iteration of Windows since Win95. Typically you want to reinstall the programs with a fresh install of Windows. Trying to install an image on anything but exactly identical hardware starts introducing more and more room for random problems like you're experiencing. The general rule of thumb is you can back up data all you want (and should have a regular backup of important stuff anyway), but programs need to be reinstalled. You're also dealing with an OEM copy of Windows which introduces even more fun if you start altering the hardware configuration.

Also, since you're copying data from a HDD that seems to have been well on its way out, all of that data is now suspect. There's no real easy way to tell how long the drive has been on the way out and if it corrupted any data as a result of its slow descent into failure. This is another reason why you always have a secondary backup.

Someone might be able to give you some suggestions on programs that can find the license keys for programs, but that too is something you should have backed up somewhere. I have a printed piece of paper I keep with my original restore media that has copies of all the license keys for the software in that little CD binder. But as long as you keep trying to move programs over without reinstalling them, you're asking for trouble. If you can't find the license keys for some of the software, you'll probably just have to learn the hard way the need for backing up important information. That's often what it takes to sufficiently motivate most people, is experiencing some kind of massive data loss or having to buy software a second time since they can't find the license key info.

Start with a fresh install of Windows, then reinstall all the apps you have the proper licensing info for. You can drag the data files over, but don't even bother with the programs on the backup drive. That will just create headaches down the road and since it's completely unsupported, plus intentionally designed not to work, you're going to be on your own to try and figure it all out. IT pros don't even bother attempting that sort of thing, because they know it's like the old maps where at the edge they wrote "Here be dragons". Also, keep in mind those data files may well be corrupt since they were pulled from a bad drive. Count yourself among the lucky ones if you manage to salvage anything at all, because many in your situation do not.