You're now in the waters of a "non standard upgrade", meaning that anything can really happen and support will be marginal at best. In order to upgrade your database you will need to fully process through the upgrade script.
You can utilize the UBB.threads System Requirements Test
to report the version number stored in your database.
How I'd tackle it would be to either snag a blank configuration file
and populate the UBB.threads database information for your server (which was made specifically for this reason), or restore one from backup so you can connect to the database, then update the configuration options through the Control Panel; again, this is what a full backup of your site will contain...
You'll have to sort through the upgrade error you indicated, where it shows files to be managed which aren't being managed, you'll need to update the "UPGRADE_CHANGES.txt" file in the install/ folder to remove the entries so they're not checked; as previously stated. I would ONLY remove files from here if you're attempting to get the upgrade script to process your CURRENT version; as files were changed in v7.6.2.
I had a complete drive failure at one of my hosts several years back, part of my recovery was to restore files from backup that I had on hand, vs waiting on the host to figure out if they had backups and figure out when to delegate them to me. I fear to know what will happen if something happens to you. I create weekly database backups and a monthly flatfile system backup, and store the resulting files on my DropBox Professional account (off site storage).
At the VERY LEAST I'd advise backing up your /cache_builders/custom and /includes folders, and the /styles/wrappers.php file; but unless you're familiar with advanced recovery I'd advise that you take a backup of all of the files in your UBB.threads install (keep in mind, if you loose your attachments or gallery folders you'll loose a lot of content, if attachments or gallery forums are something that your forum offers).