There is way too much confusion here, and you should read the moodle docs on TeX.
First off, Moodle does not come with Tex. Period. And as far as I know, there is a Moodle TeX filter, but no plugin (though SEE will I hope eventually become a "plugin" in the curent sense.
The Moodle TeX filter is bundled with a few compilations of mimetex (http://www.forkosh.com/mimetex.html) which you might be able to locate, for example, as mimetex.linux, etc.
The filter also comes with the actual TeX filter which parses material in the moodle and passes tokenized strings to either mimetex or to TeX binaries if they are accessible. mimetex is a FALLBACK, used when a TeX installation cannot be found.
TeXLive can be easily installed without root access, and the necessary paths to binaries provided to Moodle (Moodle requires convert, which is not a Tex binary, but this is a result of the filter being an antique and the filter can be amended to actually use only TeX binaries.)
Now, your first task is to determine if you were using TeX binaries or mimetex and what you want to do in future. Then you need to determine what the devil your support people did. You might want to compare your install to the file listing for Moodle for the TeX filter to see if they deleted any files (http://cvs.moodle.org/moodle/filter/tex/), and of course, the results of texdebug would be help.
As a "techie" that should all be easy enough