battery cable came loose and cleaned and replaced it. the car starts but wants to die. the air and radio went out briefly a few days before the car didnt start and I found the loose cable.

Easy way to test your alternator. Start your car then remove the positive cable from the battery. If the alternator is bad, the car should die.

Its hard to do that test if the car wants to die as it is. If the car idles low the alternator cant produce a proper voltage. AKA when it's stalling and dropping rpm's. This is normal alternator behavior to be a lower voltage at idle. I would disconnect the battery negative cable for about a minute and then try to run it again to let everything reset. A loose cable can casue voltage spikes and damage sensors or worse the PCM. Chances are if your not having to jump start the car the alternator is fine. But if you see you lights surging with a constant rpm then the alternator is bad and replace it.