Troubleshooting

I was driving my car with the heater on, windshield wipers and headlights on. The battery light came on. I kept going and the head lights kept getting dimmer, the windshield wipers got slower, the speedometer guage and rpm guage started going crazy, the power of the car was affected. I pulled off the road and made it to a parking lot and the cardied while pulling in. Needless to say the car does not start now. Is it the alternator or battery? Oh, my car is a 1990 Honda Accord LX.