Do you have an .htaccess file in the MODX root directory (or directories above it)? Problems in that are the most likely cause of a 500 error.
You can look in core/cache/logs/error.log, but if there is an error reported, it would most likely be in the Server log -- available through cPanel. MODX probably never even got started.
One quick thing to try -- using FTP, upload a hello.html file with this code to the modx root directory with this code:
Then point your browser to
http://yoursite.com/hello.html.
See if you get the 500 error there. If so, it has nothing to do with MODX.