[Blas]

When you say that "now the battery won't start the car", I assume you mean won't restart the Cobra, not the Mustang? Just like with the original battery in the Cobra...
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OK...You have verified that:
The ground connection to the battery is good.
The ground connection to the chassis back by the battery is good.
The battery cable ends are all good.
The battery has been load tested and is at the proper level of charge.
Cable connections to solenoid on firewall are good.
Cable connections to starter are good.
Ground connections at starter & chassis are good.
When running, the charging system is working properly.
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Next time the car won’t start,
I would try jumping around the starter solenoid on the firewall. Car won't start, just crank.
Use a remote start switch and jump across the 2 big cables on the firewall mounted starter solenoid. You can use a jumper cable but remember you have an aluminum firewall very close to those 2 terminals. If the car then cranks normally…you’ve isolated the problem to that solenoid or the ignition switch.