Congratulations on a fine purchase (other than the issue at hand). Rest the cabinet on its back and remove the screws (allen, I think) and the horn will pull out. I recommend you remove the woofer as well, since it will give you a visual inside as you work.
There is a chance the diaphragm is okay, as the rear switches can corrode over time or capacitors may be faulty, so it's best not to jump to conclusions too soon...
Once you have removed the screws securing the horn flange, GENTLY pull straight up. The gasket is fairly sticky on mine - exercise extreme caution during this exercise. You may need to use a putty knife or some such to pry the flange away from the gasket.