These are a bit tricky to troubleshoot, but usually something would be logged somewhere.
The first place to check is the Server Error Log in your Admin CP. Check in there to see if you accessing the media page inserts any entries in the log.
The second place to look will vary upon your hosting and server environment. But generally you'd be looking for some sort of error log which will also log PHP errors. This could be in your Apache logs or it could be in a separate log for PHP. If you don't know where this is, you will need to contact your host to help you find them.