I suppose your new site is using moodle 2.X.X
In core moodle 2 there is an editor setting that ties dragmath to Tex filter - tex filter must be enabled before you even see the icon in tinymce. So your site administrators could check first if they have installed a fully functional distribution of latex (for example TexLive) together with Imagemagick or Ghostscript (or some other tool for converting tex to pngs) and check if ticks for 3 paths of tex filter in Site administration > Plugins > Filters > Manage filters > Tex filter > Settings are green (selected binaries there executable). Usually this is not done.
If no other (optional) latex renderer is installed moodle/tex filter will try to use mimetex fallback from folder filter/tex and to make this second option available your system administrators must check that mimetex binary in that folder is executable by all users (on linux mimetex.linux, on Windows servers mimetex.exe, ...)
Third option is to use some other renderer for maths and then your system administrator needs to edit file lib/editor/tinymce/lib.php and for example replace lines
if (array_key_exists('filter/tex', $filters)) {
$xdragmath = 'dragmath,';
} else {
$xdragmath = '';
}
with
$xdragmath = 'dragmath,';
and install the scripts or filters you want to use for maths. If they absolutely refuse to install non core things you have still some options left - for example as a moodle administrator you can go to Site administration > Appearance > Additional HTML > Within HEAD and add there tags from attached file examplenet.txt and disable tex filter & change those dragmath init lines in file lib/editor/tinymce/lib.php to use dragmath with mathJax from external http://cdn.mathjax.org/mathjax/latest/MathJax.js without tex filter but with the same tokens (double dollars) for inline maths that dragmath by default adds to mathematical notations...
Universities usually do have knowledge and hard disk space for installing a full distribution of latex which allows use of tex filter with all the benefits it gives so I would suggest the first option 
- or you could as well suggest downloading a full package of MathJax from http://www.mathjax.org/ to your server and use it like with examplenet.txt tags to avoid overloading external and public http://cdn.mathjax.org/mathjax/latest/MathJax.js
