Ooh ok first of all let me say that running installed programs off that drive like you want probably won't work. When you install a program, it usually stores data in locations other than just Program Files. The two most common other places are the registry and you're user's AppData folder. Now, some programs are simple enough that they store all their data in their program files folder, but unless they're really old, very simple, or specifically designed to be be "Portable," they likely store info in some other location. Which means they will fail to run from your external hard drive.
If you want them to run like this, you'll have to install them like you normally would, and change their install path to somewhere on your external HD. This way, all the settings in the registry and whatnot know to look for the information on your drive when you try to run a program. You'll just have to make sure you're drive is always assigned the same letter by Windows, and this method should work. But just running programs off your backup? Very likely to fail.
Anyway, if it's a software that came with your HD, then it likely just made copies of all the files you told it to back up. Which means that in theory, that command I had you run should have unlocked all the personal music, documents, and videos etc. on your drive that you want to use know. See if you can access them now.
Since it looks like only system folders are still locked, I think you should just ignore them. If you want to delete them to save space or anything, I can guide you through unlocking them, though. Just let me know.
If your normal files are still inaccessible, let me know and I'll give you a better command to run.