The fact that it worked after hitting the starter points to a worn out starter but it is not conclusive. Others have found that increasing voltage or amperage to the starter by putting a solenoid relay in the system, stops this kind of problem so it is still possible that the existing wiring is old enough with poor enough connections to reduce power to the starter and your hitting the starter allowed it to get better enough connections to function with the reduced energy. I only point this out because some people have replaced their starters only to have the problem continue. If you are certain that there was power when you crossed terminal 1 and 3 and the starter still did not turn, this would point even more at a sticky solenoid or bad starter.

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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