I pull the battery (with AC) and get everything I can reach from the top. Seems to save a couple of scratches, knuckle dings and some dirt in the face. In the winter I take my fan shroud off anyway (makes washing the mud out of the radiator easier), helps to reach some alternator bolts from the top. Removing the fan, easier yet, if you have extra time and easy (less mud in the face) is more important than speed.
Check your idler pulleys, while you have the belt off. Spin them and listen for a rattle.
I pull mine and wash it out with hot water, after most deep mud excursions. Mud under the brushes will cause a no charge and eventually wear out the brushes and slip rings.
If you have no voltage (with the ignition on) at the I/F pole at the plug at the alternator (yellow wire), you won´t have any charge. Same thing with a fuseable link on the major cable from the alernator to the battery. Many times it´s worn brushes, I rarley return the core, put my new alternator in, change the brushes in the old one (a pain) and put it on the shelf as a spare.