1998 Plymouth Voyager Engine Difficult to Start and Runs Ro

Initially the battery light came on while driving and the next day the battery was dead so I recharged the battery. The car started up and ran fine. Later the battery light came back on. I figured my alternator went bad. As I drove I started to loose my headlights and other electrical components in the car. Then the car started to run real rough. It died as I pulled into the garage. I disconnected the battery cables and recharged the battery. I conneted the battery and tried to start it but it would only turn over. If I press the gas pedal to the floor it will start but runs very rough. It dies when I let up on the gas to allow it to idle. Could this all be caused by the alternator being bad?