Thanks again for all the help on this! I was just reading through the http://pondini.org/TM/FAQ.html link you sent me. I had some success with Q16, but I didn't move forward with it because I was not 100% sure I was doing the right thing. So, below are some screenshots.
Before I get to that, let me answer another question you asked me in terms of what I am hoping to get. Ideally, I was hoping to migrate over my entire User ID, along with the files with the hope that my wife and I could both have our unique Apple IDs on one computer and could just switch back and forth between users. We don't really need two computers. Having two computers dates back to before we were married. So, while I absolutely need to get to the files - the ideal situation is that I have my entire Apple ID and files. There may be a few apps as well, but we have a lot of overlap in apps. And I could always re-download apps as well.
So, using Q16 from http://pondini.org/TM/16.html as a guide, here is what I did:
1. I used Control to open the Time Machine from the dock and browse other Time Machine Discs.
2. I selected my disc.
3. I went to my back-ups folder (Sorry, that's probably not the right name for it)
4. I chose a back-up from a few days before the hard drive crash
5. I selected restore
6. And then I got this far and quit because I had no idea what I was really about to do and if it was even the right thing to do. Also, I was logged in as my wife and moment. I guess technically, I would want to do this logged in as the temporary Admin user, right?
So, was I on the right track here? Would this have migrated over my Apple ID and my files or just my files?
Finally, should this not be the right path that I am on, I do have an old external hard drive from years ago. It sounds like I could use this as well. Thanks for the details instructions you posted with screenshots.
Again, I can't tell you how much I appreciate the help! You didn't have to help me, and so I really, really appreciate it! If there is anything I can do to return the favor or pay it forward, please do let me know. Again, thank you!