Hi,
A bad cable can cause this, but it sounds more like the alternator may be failing. You are correct that it wasn't providing the correct voltage when the car was running. As far as the old cable not removed but disconnected, that isn't a problem. Do me a favor, try this load test. It is simple.
https://www.2carpros.com/articles/car-battery-load-test
Also, here is a link that explains how to test the alternator at home:
https://www.2carpros.com/articles/how-to-check-a-car-alternator
Now, I understand why you can't remove the alternator to have it bench tested, but often times a parts store will load test it on the vehicle free of charge. I would try that.
Back to the battery terminals. You do need to replace the one that broke and was repaired. If the starter would engage when the new cable was installed, chances are the new cable which is mounted on the starter, is also touching the S terminal (smaller wire) in the starter. Double check that.
________________________________
Here is a link you may find helpful if it is determine the alternator is bad. Take a look through it.
https://www.2carpros.com/articles/how-to-replace-an-alternator
Here are the directions specific to your vehicle. The attached picture correlates with these directions.
________________________________
2002 Mitsubishi Lancer ES L4-2.0L SOHC
Removal and Installation
Vehicle Starting and Charging Charging System Alternator Service and Repair Procedures Removal and Installation
REMOVAL AND INSTALLATION
GENERATOR ASSEMBLY
pic 1
REMOVAL SERVICE POINT
ENGINE MOUNT VEHICLES WITH ABS REMOVAL
1. Remove ail the power steering hose clamp mounting bolts.
2. Jack up and support the engine assembly, and remove the engine mount.
3. Tilt the engine to remove the generator.
________________________________
I hope this helps. Please let me know if you have other questions.
Take care,
Joe
Image (Click to make bigger)
Wednesday, April 1st, 2020 AT 7:27 PM