No problem helping you out. That's what a support subscription gets for you
Let's go step by step on how to answer. First, they want to know who should own the files. Since Apache (your webserver) is serving up and executing the PHP scripts, you want it to at least be in the group that owns the files. To figure out what user Apache is running as, do the following:
* Go to Help->System Info and the "PHP Information" tab
* Look for "apache2handler"
* In that section, find "User/Group" and jot down the information. Many times it's apache/apache. The 2nd word may actually be a number: apache(48)/48. Use this first value to tell them who the owner of your files should be. Tell them to update your whole Joomla directory (/var/www/vhosts/myservicematters.org/httpdocs/joomla/) to be owned by this user.
Then, you should tell them to do a "chmod u+w" to the whole Joomla directory. This enables the owner (as defined above) to write to your structure, which in this case is PHP. This will not affect other permissions (read or execute) or allow for open access to unscrupulous individuals since all write privelages should not be there already.
Certainly, let us know what they come back with and if you have more questions.
[Edit by admin: Changed some language to ensure that the user owns the files, instead of saying the group. The group is slightly more insecure and not the best recommended solution]