Check if you have mod_dir and mod_php5 enabled in apache.
ls -l /etc/apache2/mods-enabled/
Do you have php5.conf php5.load and dir.conf dir.load?
Did you do this step?
Now go to the PHP open_basedir field on the Options tab of your web site in ISPConfig and add the directories /usr/share/squirrelmail and /etc/squirrelmail (that's the directory where SquirrelMail's configuration is stored) to the line, e.g. as follows: