I have looked at your autorestore log file and I see that you have the All In One WP Security & Firewall plugin installed. I believe that plugin is the root cause for why you cannot get into your wp-admin backend WP Dashboard and the php errors. It appears that plugin is doing something with your wp-config.php file and root htaccess file. Do these steps below and let me know if you can login to your WP site.
1. Use FTP or your web host control panel file manager and rename the /all-in-one-wp-security-and-firewall/ plugin folder to: /_all-in-one-wp-security-and-firewall.
2. Delete your root htaccess file that is in your WordPress installation folder (same folder where the wp-config.php file is).
3. Try to login to your site. If you are able to login to your website at this point go to step #5
4. If you are unable to login to your website at this point then copy this file that is in this folder: /wp-content/bps-backup/quarantine/root-files/wp-config.php to this folder first: /wp-content/bps-backup/autorestore/root-files/wp-config.php and the copy the wp-config.php file to your WordPress installation folder: /public_html/wp-config.php
5. Let me know if you are able to login to your WordPress backend Dashboard at this point.
Notes|Recommendations: The All In One WP Security & Firewall plugin allows you to create backups of various files such as wp-config.php and other files. BPS Pro already does something far superior to this with AutoRestore|Quarantine. If you would like to continue using that plugin disable turn off that feature in that plugin. Disable/turn off anything that has to do with htaccess files/firewalls in that plugin – BPS Pro already does something far superior to anything that plugin does with htaccess files and firewalls. There may be conflicting features if you are using both BPS Login Security and whatever that plugin uses for login security so you will need to decide which feature to use or not use and turn off the feature in whichever plugin’s feature that you choose not to use.
Personal recommendation: Delete the All In One WP Security & Firewall plugin since BPS Pro is far superior to that plugin. BPS Pro provides all the same security protection and much, much more than that plugin offers.
If you decide to continue to use the All In One WP Security & Firewall plugin then you will need to create an AutoRestore wp-content folder exclude rule for the aiowps_backups wp-content folder. See this forum link for the steps to do that: http://forum.ait-pro.com/forums/topic/autorestore-quarantine-guide-read-me-first/#autorestore-exclude-rules