Did you copy the Moodledata folder (and all its contents) to the new server? That is critical.
Once you've done that and you still get errors turn Moodle Debugging up to the Developer level so that you see the error messages that get triggered. Those error message can help troubleshooting the real cause of the HTTP 500 messages. (HTTP 500 messages don't really mean anything specific, it's just the servers fancy way of saying there's a problem somewhere.)