[mpumas]

How did you check your alternator? The battery light is not really a battery light, is an alternator light. So if it is coming on, it indicates the alternator voltage is low compared to the battery. If it is not putting out, the battery will only last for a short time considering all the things it must power in Hondas. Use a volt meter at the battery and see if the voltage increases when the engine is sped up.