The brief
A BMW came in that wouldn't crank, the engine locked up, and on this engine that points at a known weak spot in the timing gear. The timing keeps the camshafts and the crankshaft in step, and the gear that holds that relationship is fastened together, but some of these engines still use aluminium fasteners there. Aluminium alloy breaks or deforms over the years, and when one of those fasteners lets go, the timing gear warps, the timing goes out of step, and the engine can't crank at all. A broken aluminium fastener doesn't repair, so it gets replaced, and the better part is the improved metal version that doesn't break so easily, with the engine timing reset to spec afterwards.
The diagnosis
The check confirmed it: an aluminium fastener in the timing gear had broken, warping the gear, which is why the engine wouldn't crank. The rest of the engine was sound. That's a timing gear fastener replacement, with the improved metal fastener rather than another aluminium one, and the timing reset, rather than chasing a no-crank that's really a broken timing fastener.
The work
The engine was opened up to the timing area, the broken aluminium fastener removed and the warped gear sorted, and the improved metal fastener fitted in its place. The timing was set precisely to the manual specification with the BMW special tools that the job needs, and everything reassembled, the gaskets and seals renewed where disturbed. The engine cranked and started cleanly, and a road test confirmed a steady idle, smooth running, and no warning lights.
The outcome
The engine cranking and starting cleanly, a steady idle, smooth running, the timing back in step, and no warning lights. The car went home running properly again. Replacing the broken aluminium fastener with the improved metal version means this particular failure doesn't come back, and resetting the timing properly is what makes the fix last.