Seeing if the alternator is charging is straightforward. Put a good voltmeter on the battery with the car off. A charged battery will be at about 12 volts. Start the car... with the car running, the voltage at the battery should be 13.5 volts or better. If the battery voltage doesn't increase after the car is started, your charging system isn't working.
If the charging system is OK, you probably have a large parasitic current drain somewhere in the car. To isolate it, put a good ammeter between the battery and one battery terminal. If you have a high drain, you will see it pretty easily. Now start pulling fuses one at a time until the drain drops significantly. That circuit has the offending component.
Hope this helps.

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KenP

1996 S500 W140 Coupe