Firefox keeps the bookmarks at the following location:
C:\Users\<your user name>\AppData\Roaming\Mozilla\Firefox\Profiles\e2jqfdpg.default\bookmarkbackups
The directory e2jqfdpg.default may be named differently on your system.
As you can see, in this directory, each file is a complete list of bookmarks backed up on the date as indicated by the file name. One such file looks like this:
Firefox runs the full backup of your bookmark URLs on a regular basis. The file ends in .jsonlz4. You can backup this file and import it to the new Firefox program after you have re-installed it successfully.
In fact, if you uninstall Firefox via Control Panel -> Uninstall a program, this folder will still be there.
Questions? Let me know!