there still needs to be a continuous circuit for the current. when u disconnect the battery you break that cycle.
the battery is actually what "runs" the accessories.. the alternator is just there to keep it charged.
atleast thats how ive always understood it..
pull your battery terminal.. im pretty sure your car will die. but who knows.
and if the alternator did run the accessories.. is it doing so at what voltage & amperage?

 

thanks guys for all your help it seems like it was the alternator after all

 

glad you figured it out. and now you learned something for the next time