So, you had a PC crash (or just turned it off instead of shutting it down), and at the next startup MC opened the default Library instead of the library you had been using, which you have stored in a different location.
All you needed to do was open the library you had been using previously, and all would have been good and most likely completely up to date, with only a small chance of any issues. Even if MC "forgot" about your library due to the shutdown, you could just add it back in again, MC would find the existing library and ask if you wanted to use the library it found.
But of course, backups are there for a reason. However, if they are old you can lose some work.
The Wiki is full of good information. Read this:
https://wiki.jriver.com/index.php/Library_ManagerBTW the term "Base Path" isn't associated with Libraries. The only place I can think of quickly that it is used is with the "Rename, Move, & Copy Files" function. I don't know if that's what you were looking at, but if so, you shouldn't have been for this issue.