Could the battery read 12v and still not generating enough current to start the engine?
Yes. You would see 12v on a multimeter or similiar. But when the battery is under a load, the volts would drop pretty low if the battery is bad or a connection is loose or dirty. When mechanics test a battery, they put a tester on the battery. The battery shows 12v, then they press a button on the test set that turns on a heat rod (like a toaster has) and that draws power putting the battery under a load to show its "working" voltage. On a bad battery, the volts would drop from 12v to 5v or 6v under a load.
I would say theres a 80% chance that you just have a bad battery or bad/dirty connection.
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