rsboy82: What are these plugs, can you get a picture, theres no guessing involved that way u can get a definate answer, personally i would say there is definately a fault in the charging circuit, and possibly your battery aswell, the car once started should run forever and a day off the alternator alone, u can start a car and once running remove the battery and it should run from the alternator.
Ive had a few alternators go and ive never had a battery light come on, alterntaors usually only wear out their brushes, and/or blow the diode packs, depending on what happens the light may not come on. If the brushes get low the light wont come on as its producing a charge although it will be a very low charge rate and therefore wont charge the battery fast enough, and if the negative side of the diode pack breaks down the light also wont come on.
If you get me some pictures i can identify the plugs for you, and also a simple test for you, get a voltmeter, charge the battery, take a voltage reading, and then start the car, and also check the voltage, then increase the revs and again note down the voltage. (shuld increase to around a maximum of 13.8-14.5 ish, anything around that is fine at higher RPM)