when I restored computer

What does this mean? Did you restore a backup? Did you create a backup of your profile prior to reformatting the drive?

The computer was set up to do an automatic backup every week. I know there was a Mozilla backup file on the hard drive prior to the formatting and assume it was backed up with the rest of the data. Is some kind of special backup required for Thunderbird? Does backing up Thunderbird create this Profile Folder?

The profile is Thunderbird's working store of your messages and settings. Its location depends on the OS in use.

It would be helpful to know what OS you use (Windows? Mac? Other?) and then you could be offered more precise help on finding your way around the menus and finding your profile.

https://support.mozilla.org/en-US/kb/profiles-tb https://support.mozilla.org/en-US/kb/display-thunderbird-menus-and-toolbar

An important point that the second article fails to mention is that the new Menu button isn't shown in the secondary windows: Write, Address Book, Calendar. In these windows you'll need the old fashioned menu.

I don't know why, but the regular Windows backup doesn't automatically include the folder where Thunderbird's profile is stored.

Several of these answers were helpful in understanding of how and where Thunderbird information is stored. However what finally solved my problem was my wife finding a simple procedure on the Internet for locating the profile folders. Once I found the two profile folders one new and the one that was backed up, I simply replaced the new folder with the backed up folder and got 99% of Thunderbird back. Three local folders are still missing but I'm working on finding them. My question/problem has been solved.