Actually, not running 12.6 is good (it is 12 volt battery) when running, the ideal voltage is 13.8. If the battery has 12.6 and
there's not even a click it's either a bad connection or an interlock problem (which would include an security system lockout). I
have seen cases where the battery had internal problems, it would show voltage when just sitting, but any attempt to draw starter
current and the voltage would suddenly drop to 1 or 2 volts. Most of the time, you will get some sort of click as the small amount
of stored power is consumed. So measure the voltage while trying to start it, also you would see the lights at least dim if that
were the case.

One thing to do is get a starter bump switch (maybe borrow one) and see if the starter works on its own. But, don't be under the car
when you test it! Measure the voltage reaching the solenoid when you turn the key.

Dennis