What I would do first is visit each page in the front end of the site in a browser. On each page, type Ctrl-S and save the page to a separate disk file on your local machine. That way, if everything else fails, you can create a new account and put them up as static pages, or base a new site on the HTML from the pages.
If you have cPanel access, you should be able to regain control of the site.
In cPanel, in the File Manager utility, look at the MODX root directory (the one containing the assets and manager directories). Report back on whether there is a core directory there or a config.core.php file. That will help determine which version of MODX you're using.
Once we know the version, we can PM you further instructions rather than providing public advice on how to break into a MODX site.
Just a thought, before going to all that trouble, did you try the MODX username and password you were given on the Login page you get to by putting
http://yoursite.com/manager in the browser's address bar?