If you have access to a volt meter, measure the battery voltage (should be at least 12 volts) then start the car, the alternator should be putting out around 13 volts. If there is no change after you start it the alternator isn't putting out any voltage. The regulator could be bad or the alternator could be bad. See if you have voltage at the field terminal (the small spade connector) of the alternator. If you have voltage I would suspect the alternator, if not I would try a voltage regulator.
Good Luck,