You surely need to have both engines off and parking brakes on before being able to call GSX. However, if you don't, you are supposed to see a message *and* a sound, to warn you you can't call GSX unless you turn off the engines and set the parking brakes.
if you only hear a sound, it means GSX is trying to tell you something, but you don't see the message, because messages has been disabled in the Info settings of the sim.
if you don't even even get the warning sound, but you DO see the GSX jetways, it's seems GSX is loading, but for some reason hasn't recognized the airport. Do you see the "Airport cache loaded successfully" message when starting ?