As a general rule a new battery is not actually fully charged, no matter what the packaging or anyone tells you. 12.6 volts is below par and I recommend you charge it, using a proper battery charger, not a tender. That is best done off the bike.

As for connections, disconnect the other ends of both main battery cables, clean and refit, ensuring they are tightly secured. Use a little dialectric grease to keep damp out. Until the battery is fully charged and able to deliver full performance we cannot diagnose any remaining problems.