Dying C4 Alternators
C4 alternators are a pretty weak design in the first place. You should not jump start a dead battery with jumper cables and then rely on the alternator to charge the battery back up. You should slow charge the battery back to life first with a battery charger. Using the alternator to charge a depleted battery up places a heavy load on it, overheating it and you may burn out diodes. Then you end up with a low voltage output, as some have experienced.
To verify your battery is still good and does not have a weak cell, chrge your battery overnight on a two amp charge rate with a regular battery charger ($40-60 Pep boys models work fine). I would not rely on a trickle charger to get a dead or near dead battery charged back up.
With a voltmeter, veryify the voltage when the charger is hooked up and charging the battery. It should be 13.5-14 volts.
After the overnight charge, disconnect the charger and measure the voltage on your battery terminals. This voltage will rapidly decrease for a little while. Note the first voltage measurement (with the charger disconnected, it should be about 13.0-13.2 volts, but may drop down to 12.6-12.8 volts 60 minutes after you have removed the charger).
To verify that you do not have a significant resting current drain on the battery, you can measure the battery terminal voltage at 12 hour intervals (do not start the car or operate any accessories/lights, etc.). If the battery voltage drops more than .02-.05 volts per day, I would be concerned about something inside the car that is draining the battery. There may be a better rule of thumb for voltage loss under storage conditions, but that has been about my experience.
You can also disconnect one of the battery terminals and measure the at rest current draw with a voltmeter/ammeter. Just change to scale to amps or 500 milliamps and connect the probes to the disconnected cable and to the battery post you just disconnected it from. The current draw should be around 50 milliamps or less. Less is better, because your connected up battery will last longer with a lower current draw.
I am not sure what the best alternator is for a C4. Has anyone actually found/used a good heavy duty replacement? The CorvetteClinic link doesn't have any technical details on what they have done to improve the design (perhaps the better cooling fan design helps).
A good alternator will produce about 13.5-13.8 volts with engine rpms above 1500. With a good battery in the car, less voltage means weak or dead diodes inside the alternator.
I went through about 4 alternators on my 86 in 8 years. I could eventually change them in the parking lot of an auto parts store in about 10 minutes. One of my four failures was right after using the alternator to charge up a nearly dead battery just after a jump start.