I think this was still on the login screen. There were no unusual dialogs.

Here's what happened:

My computer locked up except for the mouse cursor

I restarted lightdm using the console (Alt-F2)

I logged back in. Every thing was fine.

I get up to check something downstairs in my house.

I come back and it's in the console (black screen, white text, DOS-looking place). It's displaying some messages like when you shut down the computer in Linux. The part where it checks to make sure everything is shutting down properly.

Except I did not shut down my computer. My old password was displayed in the middle of the screen.

I tried doing sudo service lightdm restart as designated in this answer:

But nothing happened. So I just powered off my computer and turned it back on. From that point everything worked normally but I am not sure as to why that happened. That was why I changed my password just to be safe.