Very odd situation.

The AC being on should not drain the battery. I don't see a connection there to the no start.

Did you try to start the car AFTER you coasted into the gas station and BEFORE you jumped it? Any chance the car was not in neutral when you tried to start it during the no start? Perhaps there was some other random intermittent ignition issue.

Yes, 13.9v means the charging system is working....at least during the test. It still could be an intermittent problem.

Before buying a new battery I would load test the old battery. Autozone and many parts stores will load test them for free.

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2009 ML320 Bluetec
1985 300CD
1981 300TD

Past Mercedes
1979 300TD
1982 300TD
2000 E320 4Matic Wagon
1998 E430
1984 300SD
1980 300SD