You're bypassing the ignition switch, not the solenoid. I'd jump the wires going to the NSS and see if it starts, if so, then you'll know its the NSS. There are threads on here on how to jump the NSS up above the driver's kick panel but I think they all apply to the 123. Search on purple wire NSS and I think they should come up.
It could be a problem in the key swtich. That's not unusual.

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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