Bought a 85 300z turbo , ran great, for about a week , got in it oneday wouldn’t start , no crank , bought a new battery, when installing smelled something burning. same prob. Won’t start ,
The burning smell was probably a fusible link that burned up. On the passenger side of the engine compartment near the firewall, there's a box that contains six fusible links. One of them is probably burned up; by looking at each one, you should be able to see the bad one. Disconnect the battery and use a multimeter to find the short to ground. You can download a copy of the FSM for your car from this site:
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