2002 Chevrolet Impala Starting the vehicle.

How did you test the generator and what were the results? It is fairly common on GM vehicles starting with '87 models to go through four to six replacement generators, but to reduce the number of repeat failures, you need to replace the battery at the same time, (as you already did), unless it is less than about two years old.

To start with, use an inexpensive digital voltmeter to measure the exact battery voltage with the engine off, then with it running, then post the result in your reply. The second half of the test requires a professional load tester.

A good, fully-charged battery will measure 12.6 volts. Your 12.9 volts just means there's a surface charge that can be removed by turning on the head lights for a few seconds.

13.93 with the engine running is okay but it's on the lower end of the acceptable range. We want to see between 13.75 and 14.75 volts. I need 14.5 volts to be happy.

I'm not sure what you were doing "when testing from battery to alternator", but up to 14.75 volts is dandy. That's as far as you can go by yourself. The second half of the test involves measuring full-load output current and "ripple" voltage with a professional load tester. Also, if you just finished charging the battery with a portable charger, the starter should be cranking just fine. If it's still slow, your mechanic will also measure starter current draw. If current is considerably higher than normal, suspect a defective starter. If current flow is normal, as in around 100 amps, but it still cranks too slowly, interpreting the results gets a little tricky. It may be easier to, ... Boy, I hate to say this, ... Replace the starter as a test. All starter motors are actually two motors built into one housing. If one brush is worn and not making good contact, the motor will be less than half its normal strength, will crank too slowly, start out drawing half the normal current, then due to its slow speed, current flow will approximately double and falsely appear to be normal.

If full-load output current is low, suspect a failed diode, and that can be blamed on the old battery. This generator design is known for developing huge voltage spikes that can destroy the diodes, the internal voltage regulator, and interfere with computer sensor signals. The battery is responsible for damping and absorbing those spikes, but as the lead flakes off the plates, as it ages, it loses its ability to do that. That's why there's such a problem with repeat generator failures unless the battery is replaced at the same time unless it is less than about two years old.

With one failed diode of the six, all you'll be able to get is exactly one third of the generator's rated maximum current. 30 amps from the common 90 amp generator is not sufficient to run the entire electrical system under all conditions. The battery will have to make up the difference as it slowly runs down over days or weeks. With a bad diode, ripple voltage will be high too, and that is measured by the load tester.