From what little I can understand, it sounds like the charging system is not recharging the battery. Charge it with a home battery charger at a slow rate for an hour, then try to start the engine. If that works, measure the battery voltage with an inexpensive digital voltmeter. With the engine off, it should read 12.6 volts if the battery is good and fully-charged. If you find closer to 12.2 volts, it is good but discharged. If you find it is around 11 volts or less, it has a shorted cell and must be replaced.
Measure the battery's voltage again while the engine is running. It must be between 13.75 and 14.75 volts. If it is, that just means it is okay to perform the rest of the tests, but that requires a professional load tester to measure "full-load output current" and "ripple" voltage. If output current is one third of what it should be, the generator has a failed diode and must be replaced.
It is important to understand that since GM redesigned their generators for the 1987 model year, they develop huge, harmful voltage spikes that can destroy their internal diodes and voltage regulator, and interfere with computer sensor signals. It is not uncommon to go through four to six replacement generators in the life of the car, however, the battery is the key component in absorbing and damping those spikes. As they age and the lead flakes off the plates, they lose their ability to absorb those spikes. Therefore, to reduce the high number of repeat failures, any time you need to replace the generator, always replace the battery at the same time, unless it is less than about two years old.
Monday, December 5th, 2016 AT 10:30 PM