Put a voltmeter on the battery & start switching on loads (fan, lights, etc) & if the voltage drops too low, you may have a problem. They normally run at around 14V but will drop slightly under load. If it gets too close to 12V (battery voltage) you could be in trouble. First thing I'd check is cables & terminals, then brushes, then regulator. If your alternator is dead, I'd highly recommend a Bosch one for ease of repair in the future. They have a combined brush and reg unit which screws on the back. You can pick one up from the wreckers real cheap. I think I paid around $30 for a 55A unit from an XB.
Evan.