This tells you:
Warning: file_exists(): open_basedir restriction in effect. File(/var/moodledata/) is not within the allowed path(s):
/var/moodledata the data folder for Moodle is not within the directories allowed by your PHP setup.
An allowed path (one of them ... they are separated by ':'s)
/var/www/clients/client1/web1/
Is that where the moodle code exist? or is the moodle code in a folder called moodle in /var/www/clients/client1/web1/?
What if you manually created moodledata in /var/www/clients/client2/web1/ directory and made sure the apache user/group as access to moodledata to be able to read/write?
So moodle code is in a directory called moodle in /var/www/clients/client2/web1/moodle/
and the data folder for moodle (called moodledata) is also at that same level:
/var/www/clients/client2/web1/moodledata
Set the document root for that to /var/www/clients/client2/web1/moodle/
Truth in attempting to assist ... don't run ispconfig. So don't ask me how to change ispconfig configuration, but, rather consult with ispconfig folks.
If one Googles for that error ... one can see there are issues with other software as well - depends upon how systems have been setup/etc.. ... so this is not necessarily restricted to just Moodle:
http://lmgtfy.com/?q=debian+Warning%3A+file_exists()%3A+open_basedir+restriction+in+effect.
'spirit of sharing', Ken