Turn on your headlights and try to start the car. The starter takes more current than everything else combined. If the lights do not dim at all, could be a loose connection at the starter (where the solenoid is mounted). If the lights immediately dim or go out, check for a bad connection at the battery or at the ground connection to the block. It wouldn't be the first time a voltmeter showed the battery as good, but the connection wasn't good enough to pass current to the starter.
If the starter has a bad winding, you can have a "dead spot" where it will start the car fine as long as it can begin spinning before hitting the "dead spot", or more correctly, the dead conductor on the commutator. If the starter stops on the bad spot, it cannot get off it to turn. I actually had a brand new S10 pickup with the 4.3L do this with less than 3000 miles. The symptom was that everything was perfect, good voltage, lights lit up, just total silence from under the hood when trying to start.