With the engine running and the battery being charged there should be ~13.8 volts across the battery. If there isn't, then the battery isn't being charged properly, and you would suspect the alternator.
If the alternator is providing 13.8v to the battery, but it's not holding the charge, then the battery is faulty.
You can also test for current being drawn while the car is off. The battery and alternator could both be OK, but a wiring fault could be draining the battery when the car is supposed to be OFF. If that's the case you can pull fuses until you find what is sucking the power.
You need to get a bit CSI on the car and work out what is actually happening.
Take the 12 volt battery to any store that sell new ones *other than Auto Zone. Ask for a free 15 second battery *load test to see what the reserve amperage capacity is. Amperage spins starter motors not voltage.
When you're sure a fully charged battery is in the car start it and touch the battery terminals with an inexpensive volt meter set @ 20 volts. IF the alternator is charging properly, the volt meter should read between 13.5 - 14.2 volts.
You should have gotten an inexpensive battery amperage draw test which tells the "health" of the starter motor.
Usually a car will not run if the alternator is bad...The battery ONLY starts the car...after the car is started the alternator provides ALL of the power to the car. Those machines the auto shop use often give incorrect results. The battery must be fully charged for it to be tested. If the battery is older than five years then it is junk...
You can't test a discharged battery. But, if a mechanic got the car running, he can easily measure the output of the alternator and determine that the alternator is not charging (which might be caused by the alternator, itself, or by the voltage regulator).
I would believe the people who tested the battery and said it was good, and I would believe the people who told you that the alternator is bad.
By the way, it might be cheaper to shop for an alternator online, then get some neighborhood mechanic to install it for you.
After reading your ordeal I'd suggest if you want to be able to rely on your ride just take it to the dealer. You already wasted the money replacing a perfectly good starter. Whoever the "mechanic" was that told you the battery was OK could have taken another minute to diagnose the problem. That was not a mechanic...it was a lube boy or tire changer!
The alternator is the thing that charges the battery when the engine runs. I suspect that if the battery is good, then you change the alternator. Don't choose a cheap one because it won't last you long. If that still doesn't work, change both.
Don't just go replacing things randomly. Get the alternator checked. Not sure why the supposedly called "Auto Shop" didn't check that for you so you could tell what was wrong. Take it elsewhere as they soind like they are either lazy or idiots.
If you have a battery light popping on when you start your car than you have a charging issue, meaning your alternator is bad cause its not staying charged
Get The alternator Tested.Its leaking through the internal diodes
More than likely it is the alternator if the battery is good
I have been having problems with my car, at first it would have a huge problem to start so I went and got a new starter. Now everytine I go start the car the car is dead I always have to jumpstart the car . People tell me it could be the battery but I went to an auto shop and told me the battery is good. I have other people say it's the alternater.