I'm looking at an 83_300 elec wiring diagram's starting circuit. The path for power to the starter solenoid starts from the battery > terminal block on pass fender > light switch (terminal 30) > ign switch > NSS > starter solenoid. A sticky solenoid, or bad connection(s) bad wiring at any of those components can cause the problem you're having. I'd start by putting a voltmeter on the starter solenoid terminal and measure voltage when it is energized. I'm not sure what it should be but my guess is not lower than 11 volts. If you jumper the solenoid directly to battery + terminal and it cranks, then you know you have a bad connection or component somewhere along that path

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85 300D turbo pristine w 157k when purchased 161K now
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83 240D 4 spd manual- parted out then junked