I'm having the same thing happen to my '98 Integra, but when I have the battery and cables connected to a charger, I noticed that my taillights start flashing red. The engine won't turn over and the ABS and Seatbelt lights also come on. I'm gonna be checking the cables and starter after it stops raining, then doing a bench test on the batt and checking the alternator later.
Anybody have any other suggestions for this?