1998 Plymouth Breeze Battery loses power but Alternator is

Hi there, I have a problem with my plymouth. Last night I blew out the starter motor which I changed this morning. After charging the battery back up I was able to start the car without any trouble. In fact, the car started fine throughout my entire pizza delivery shift, but I was noticing something a bit strange: after driving for about ten to fifteen minutes the battery light would come on in my dash. Taking care to pay attention to the warning signs such as the radio cutting on and off, the lights dimming, and general shutdown of the car, I didn't run into any of these problems. When I would return to the parking lot I did a quick check to see if the car would start again after I turned it off, it did, the battery light would flash on as it usually does upon ignition and it switched off after about three seconds. So I thought maybe it was a fluke and something just happened that corrected itself when I restarted my car. Wishful thinking, I know. So I made it through the shift, noticing this random battery light, each time happening around ten minutes into my delivery. So time came to go home. Before I left I checked the connections to make sure nothing had wriggled loose during my shift and, feeling satisfied with my findings I left and started home. On the way, about ten minutes into the drive, I noticed again, the battery light. But again, I didn't notice any loss of power to my systems, thinking the entire time, if its my alternator I would be losing power, optimistic, I know. So I continued to drive, worrying the entire time that I'd end up stranded, but I didn't. Finally I arrived home, turned the car off and took a deep breath turning the key back into the on position. Nothing. Not the sound of the radio not a friendly click of the ignition, not a ding reminding me that the car is alive, not a thing. So I'm thinking, awe man. What am I going to do now, still thankful that I was able to make it home.

So the problem is this. Car starts, runs fine for ten minutes or so, battery light comes on, runs on the alternator until powered down and then nothing. Any incites into this phenomenon would be greatly appreciated.