More information/description of your system/server is needed.
It's remotely hosted ... that much is known, and you don't have command line access, but ...
Who is hosting provider? (what company do you pay to host site?)
In whatever control panel they provide you have you been able to determine if the package you have purchased (your account) supports the requirements for Moodle? PHP version and MySQL version.
Those requirements are briefly listed on the http://download.moodle.org/ site.
Version 2.5.x, for example, requires: PHP 5.3.3, MySQL 5.1.33
If hosting provider does NOT have those versions of PHP and MySQL available to their customers, seek another hosting provider that does.
No one can help giving specific things to try without some more information.
'spirit of sharing', Ken