You should probably remove the cables from the battery and clean the terminals and cables, then re-install making sure the cables are secured well to the battery posts.
The hydrometer green eye are not that reliable, so I wouldn't trust that just because it's green means the battery is fine. Your local auto parts store is probably able to perform a load test on the battery. You could also have an intermittant open circuit within the battery causing your problems too.
-Rod