Ignition switch contacts implausible - some are on and some are not when they should all be the same. Given that you mentioned you're starting it with a screwdriver, that seems entirely plausible.
I'd probably look at changing the whole ignition switch assembly - this bit:
That requires dismantling the cowling, which you've probably already done, removing the steering wheel, clock spring and column stalks. Then you have to grind these two shear bolts off:
Usually I'll cover the interior with some thick cloths / rags / old blanket and cut slots in the bolts with a dremel, then chisel them out.
At this point its probably easier to swap the whole chunk than to try and change bits inside it.