I have used Cpanel to generate and install a self-signed certificate for HTTPS and now that I have installed phpMyAdmin once I access phpMyAdmin via HTTPS it throws out an error 500 message.
Why is this?
One thing you could test (although first I would follow LazyOne's advice and check the error logs) is that you have a vhost set up for listening to SSL traffic, it could be that your server is listening on the right port but once traffic comes in it isn't being handled.
An example (borrowed from here, slightly changed by me) would be.
cPanel should handle this but I am not sure if it always does it correctly.