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If by rotating the switch with a screwdriver you could start, but not with it installed & using the key, the problem almost certainly lies in the switch itself. I had the same issue on my '83. The PO, my grandfather, had a no-crank no-start problem that the dealer "repaired" by rebuilding the starter, asserting that it was worn out. This, on a garaged car with 70,000km. So $250 later, still the occasional no-start, eventually it became all the time. I too carried a screwdriver to start my car by jumping the solenoid terminal. (By doing that you've already established that the problem isn't in the starter or the solenoid. So it's either wiring - unlikely - or the switch.) Finally I took my switch apart by prying out the crimped edges on the casing and bent the rotating contacts down very slightly, just enough that there'd be a more solid connection. Stuck it back together and tapped the crimped metal edges back into place --- that was in 1996. Still good, 65,000km later.
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Chris, Dartmouth NS Canada 70 M-B 280SE, 83 245DL, 84 244 turbo, 90 780 turbo, 92 VW Golf, 90 740 Rex/Regina