In full:
Warning: file_exists(): open_basedir restriction in effect. File(/web/conf/gd-wordpress.conf) is not within the allowed path(s): (E:/Data//bang-olufsen-repair.com\;C:\Windows\Temp) in E:\Data\bang-olufsen-repair.com\testsitetestground.com\wp-content\mu-plugins\gd-system-plugin\class-gd-system-plugin-config.php on line 78
Website runs on a shared server as you'll no doubt notice, was updating plugin when it seemed to just time out then everything has been out of action since then on the testsitetestground domain.
Server guys don't know what the problem is as their backups aren't fixing it and site now displays "Error establishing a database connection" First time I've encountered a problem such as this so any help is appreciated.
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Warning: file_exists(): open_basedir restriction in effect. File(/web/conf/gd-wordpress.conf)
This error is showing because the server is restricting your access to the /web/conf directory. I'm assuming you are seeing this error as a surprise because you are supposed to be accessing a relative path (web/conf) instead of an absolute path (/web/conf). A prefix of / makes a very big difference.
If your site was running from /var/www/html, a path of web would be at /var/www/html/web, while /web would try to access the web folder in the root directory of the server.