The only other thing that I can think of is that the battery puts out the required voltage but not amperage. Edit: Take the battery to your local auto parts store for testing.

 

You could have an open in the ground side of the circuit. Measure right at the starter, with the minus wire of the meter on the starter and the plus on the terminals. If you have 12 volts on both terminals at the starter, measured to starter ground, and it doesn't turn, it's a bad starter.

If you find less than 12 volts there hold one wire on battery minus and then probe the terminal, the wire, the transmission, and the starter to see where the voltage is being dropped. There should be much less than 1 volt across any connection.

 

I got it working this weekend. I overlooked the battery ground to chassis. I realized it was smoking when I turned on the radio and high beams and tried to the start the car. I cleaned and sanded the bolt, connector, and chassis, and now it works great.

Thanks for all the help!

 

A keen observation pays off. Congrats.

 

I figured I would add this too for anyone who searches this in the future:

I had a similar problem when I was getting my car dyno tuned. Did 3 passes on the dyno and then went to start the car for the 4th pass and had nothing at the starter (radio came on, cooling fans came on etc etc). My tuner and I were both seriously puzzled for like 15 minutes trying to figure out why it just wouldnt start.

Ended up being the transmisson ground wire to chassis. Came undone from transmisson so my engine wasnt grounded. I had removed the valve cover one a few days before and forgot to reinstall it.

Reconnected the ground to transmisson and car ran great!