Won't start
If there is someone near you with a Z, see if you can swap your cam angle sensor with theirs as a troubleshoot. The CAS is the round metal sensor on the front of the engine, driver's side, coming through the timing belt cover. It has one electrical connector coming into it. It is possible that the CAS is going bad, and if so it could cause the problem.
Also, the one recall for the 90-96 300ZX was the PTU, power transistor unit. It's the small black box on the passenger side timing cover, with a 6-7 wire harness coming in one side, and out the other. The early ones were known to overheat and fail, and the car would start intermittently or not at all. Your car likely has the updated version of it, but it can still fail. It would be worth trying to swap that as well, to see if that fixes the issue. If either of them do, you can buy that part from www.z1motorsports.com either new or used, and install it.
A note with the CAS - it's keyed to go on in one position only, but since the cams rotate at half the frequency of the crank, if you install it and the car starts, then peters out and dies, then you have it 360 degrees out of phase. Remove it, spin the shaft one full revolution, and reinstall it, and it should run.
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