04 Accord cranks slow when damp. Battery is new.
 

My 04 Accord cranks slow when it is damp and after about 12 seconds of cranking, the battery is (or appears) dead, and I just get the "clicking" (like a dead battery).

1) The battery is new. I had Auto Zone test it and they said it is working fine.
(terminals are spotless).
2)AZ also said alternator is excellent, and I see that it puts out about 14.4 v.

It always starts great when dry, but if I let it sit "for a day" in damp weather, it will crank really slow and dead. If I put on battery charger for a half hour (on 8 amps), it will then start again.

If it were the starter, I do not see why the battery would die after about 10 secs, and then I get the clicking (like a dead battery).

Any advice would be greatly appreciated!