If battery is showing 12.7 volts two things come to mind.
Try cranking / putting on a load. Still showing 12.7 volts? Start checking connections. Battery, alternator, grounds etc. All the usual suspects. You can have full voltage but a loose or corroded connection won't allow the amps necessary.
Try cranking, voltage drop after putting a load on it? Probably bad battery. Load test if possible before straight out replacing. But like
@fortrdb said, if its older its probably time to replace.
Those would be where I would start.
My .02 worth.
Nate