I had a similar issue on another car and it took a while to find but it was a cable to the starter relay that had got water inside the casing and corroded the wire ! no outward signs of any problems, just took ages checking continuity until i found it.. problems can be that random
good news it turns over
these lips were an optional extra from nissan when new, i had one on my 350z, aftermarket fitment can be an issue though, I had to buy a replacement and the first one delivered didn't fit !