If you read Debugging you can get more information. You can copy the debugging lines from config-dist.php to config.php and uncomment them.
However, it's very unlikely that the Error 500 was not logged *anywhere*. You would need to tell us what operating system you are running and what web server. Personally I would go back to your server admin. A server that throws an Error 500 and does not log it is not set up properly.