Vista and 10 are mostly the same in that your Firefox data is under

C:\Users\username\AppData\Roaming\Mozilla\Firefox\Profiles

AppData is a hidden folder, so make sure Windows is set to show hidden files and folders:

https://support.microsoft.com/en-us/help/14201/windows-show-hidden-files

Since profile folder names are very unique, simply copying the old folder from one system to the other will not make it visible to the new installation of Firefox. The most convenient approach will depend on whether you want a subset of data (e.g., bookmarks and passwords) or much more.

Wonderful! "AppData is a hidden folder" was the missing link. Now, how do I add the bookmarks from the most recent old computer backup to my new Firefox bookmarks? I see where they go, but just copying and pasting to the right location does not seem to get them recognized?

Your "live" bookmarks are in the places.sqlite database file along with history. You could transplant the old database file in place of the new one or, if you don't need the old history, you can use the "Restore" feature to apply one of the files from the bookmarkbackups folder to the new database. This article has more info: Restore bookmarks from backup or move them to another computer.

Thank you so much! I used the Restore function. Luckily we did not have many new bookmarks that would be difficult to replace.

Idea for a valuable feature; make a way to add or merge an old backups file with an existing one. So nothing is lost?

Thank you Firefox! Anything that helps keep us safe from the evil (and incompetent) clutches of Microsoft is great!