Because the operating system won’t recognize it. In the old days you could do it with a DOS program, but for Windows you typically have to reinstall. Check the downloads folders and see if you can find the executable you downloaded when you did the initial install. You should be able to reinstall the software on the new PC.

But I was having power issues with the computer, not profile or password problems. I don't know jack but when I did this the hard drive acted the same as it did when it was in the computer. If the problem is actually the software I would think it will still be there.

In the past, I backed up windows computers by booting off a Linux cd and copying from one drive to another.

It was one command. But just to suggest that idea: Booting off an external drive if there's a bootable operating system on it and you can set the BIOS to boot off that drive at startup.

Mainly, no drives had to be moved.

Frequently. Either in an HDD case or in a drive dock which makes them pretty easy to swap around, because there's nothing to open.

Something I've noted is that the external HDD cases fail with regularity while the drive inside is still good and can be moved to another enclosure with ease.

you cannot access it as an external drive. Many of the newer computers are sold with the hard drive encrypted.