hmm, Sounds like the battery could be bad. It is very possible for a battery on it's way out to read 12.5 volts while sitting and still not have enough juice to do much of anything. While you have your multi-meter out measure the battery voltage while someone inside tries to start the vehicle. If the voltage at the battery drops to 9 volts or below the battery is most likely bad and should be replaced.
If on the other hand, the battery voltage doesn't drop look for a loose battery cable or bad connection somewhere.
also, you didn't mention how old the battery was, if the battery is original replace it.
Good Luck,
Saturday