[poorboy]

Do you have a ground wire from the engine to the frame? If the solenoid is mounted to the firewall it needs to be grounded to the frame. No, the starter does not have another solenoid on it.
If you have a battery disconnect switch shut it off, connect the wire from the starter and the battery cable togeather, then turn on the disconnect switch momentarily. The engine should turn over, if it don't I would say the starter is bad. Auto Zone starters are junk!

Poorboy