C230 Alternator Dead?

[benzer2]

Hi:
I will make it short and sweet.

Car has been starting a little slow for a couple of months. Car used only
on weekend runs of about 1hr highway (30 min each way).

Car started on Wednesday and ran for about on 40 minutes while I was cleaning garage.
Car would not start yesterday. I started by jumping, first attempt no go, second attempt car started. I removed cables and then the car ran for about a minute, and then died. Battery would not restart car.
Tried jumping again and had same sequence of events.

Does this sound like an alternator not working, or could it still be a battery problem?
Car is 1999 C230 Kompressor, only about 5600 miles.
Car is on its second battery.

Any assistance is appreciated.