Yes, the inability to turn over points to a weak battery. However, the stalling after starting isn't explained by a bad battery. I have experienced that symptom when I've had summer fuel in winter conditions. What temperature is it at your location and are you running winterized fuel?

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13