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The backup archives are where you have configured them to be stored. By default, that's the administrator/components/com_akeebabackup/backup directory. If you have set up the backups to be transferred to an off-site backup location then the backups will be there as well, or instead of the backup directory.

Please note that your backup log file was not uploaded, that's why I can only give you this generic reply. If you could please put it in a ZIP file and attach it to your next reply I can check what the log file says.

First, please confirm that you have the .jpa, .jps, or .zip backup archive file in the default directory in the file system. If you only see a .php file, that's just the log file.

Then, download Kickstart Core from our Download page (there's a link to it at the top of every page of our site).

Extract the ZIP file you downloaded on your computer.

Upload kickstart.php to your site's root.

Rename your .htaccess file to .htaccess.bak. You may have to click on "Show hidden files" or something similarly titled in your FTP/SFTP software, or your hosting control panel's file manager to see this file; all files whose name starts with a dot are hidden files in Linux.

Make sure you have the connection information to your database. If unsure, ask your host. If you are creating a new database from scratch please make sure that you create a database, create a database user, and give the database user full permissions to the database.

Run Kickstart by visiting the /kickstart.php URL on your site.

Kickstart should automatically find the backup archives. If not, check the Archive directory option at the top of Kickstart page. Append (add to the end of what is already there) /administrator/components/com_akeebabackup/backup and click the green Reload button.

The Archive file drop-down will show you the available backups. Select the backup you want to restore.

Scroll all the way down and click on Start.

The rest of the process is what is shown in https://www.akeeba.com/videos/1212-akeeba-backup/1618-abtc04-restore-site-new-server.html.

Your backup archive contains your database and your site's files, along with the restoration script.

If you want to only restore the database, it is possible, but any updated extensions might not work because there will be a discrepancy between the code running (provided by files, newer) and database structure (restored from the backup, older). Therefore, I recommend restoring the entire backup as I told you.

As you can read in the documentation and see in the video I linked you to the restoration takes care of restoring the database and re-configuring your site (change the configuration.php file as necessary).