First of all with your battery voltage reading 11.4v means your battery is draining. Very likely from being used but not charged. Do you have an external charger you could use to keep it fresh?
So you've got battery voltage to the starter.
And with a good engine ground strap, you probably have a good ground to the starter and solenoid.
If the above two things are true, and your starter is good: try a jumper from the terminal where you have voltage, to the third terminal on the solenoid that comes from the ignition switch. This should engage and crank the starter, turning over the engine. CAREFUL! Make sure your transmission is in neutral! I don't want you moving the car!
If the starter does not crank when you jumper it, I'd want to know what happens to the voltage reading at the starter's large battery cable when you try.
Let me know what happens when you try the jumper?