I don't think we know that for sure. Are you referring to the 12.7 V after charging? That's an indicator, but doesn't really test how strong it is. A better test is with a hydrometer, and the best test is under load.
A crude way to check power under load is charge the battery, then watch the battery voltage while it turns the starter. If its above 9.5 V it should be good enough to do the job.
So then the problem is the wiring? :poke:
Lets hope new is good but we know thats not always so. :(