To the mail log: amavisd is not running and without amavisd you will not be able to reaceive or send emails. Please run:
and check the mail log again.
The entry in the system log are fine.
And the ISPC log complained about the php_admin values in the vhosts, which I commented in the template now to be able to start Apache, the search noted that this could be because PHP is not installed, but that's not the case at all sadly.
Then you really dont have mod_php installed and this explains the problems with php in your sites too. Please make sure that you followed the perfect server instllation guide for ispconfig 3 and ubuntu to the line or your system will not work properly.