At first on screenshot I see that you've got some issue with custom translations. Go to the data/Base_Lang/custom, backup and remove all files there.
According to the update, please do it in the steps, because making such update from 1.3 to 1.8 will fail for sure.
I propose something like that, but if you'll have some issue try, to update to the lower version.
1.3 -> 1.4 -> 1.5.0 -> 1.5.4 -> 1.6.0.
When you'll have 1.6.0, then copy update.php from the latest release as up.php and use this script to automate above steps.
Also it would be great if you could update on clean copies. I mean that do not extract over the existing sources, but extract EPESI to the empty directory, then copy data dir to the clean copy.
All errors during the update may go into main server logs, data/php_errors.log, data/logs. Also please review patches log, which location has changed and it'll be in data, then in data/logs.
Also please note, that versions below 1.8. won't work on PHP 7, but it's still rare to have PHP 7 installed.
Best regards,
Adam
