Slowcoach, welcome to the forums.
Think you will find what is happening is that the onboard 3200 is the default and most likely hardwired to the external port, and that is why you can't get an external monitor to run off the 3650.
Might want to have a read here,
Asus M51Ta Owners' Lounge
and see what other owners of the same laptop have to say (48 page thread).