The timing chain is a heavy duty chain inside your engine, which is connected between a sprocket on the crankshaft, and another sprocket on the camshaft. Its purpose is to coordinate the action of the camshaft (which opens and closes the valves, and also drives the distributor) with the position of the crankshaft (which moves the pistons up and down in the cylinders).
When the timing chain jumps out of mesh (which it will do when it becomes too loose due to age and wear) the synchronization between the camshaft and the crankshaft is disturbed. When that happens, the distributor rotor, which is driven by a camshaft gear, will shift to a different position than where it belongs. The change will usually be equal to about one cylinder ahead or behind in the firing order. The igntion system will still produce sparks, and the injectors will still spray fuel; but because the camshaft has gone out of time, the valve timing, sparks and fuel injection will not take place at the right position of the crankshaft.
That is why the engine will not start. If the spark plug wires are moved to the newly changed position in the firing order, the ignition timing will then be right; but the engine will still not run, because the camshaft is still out of time, and it is now opening and closing the valves at the wrong position of the crankshaft. The only way this problem can be fixed is to remove and replace the old stretched and worn timing chain, and probably also replace the worn sprockets. When the new chain is installed; the position of the camshaft and crankshaft must be carefully re-aligned with the manufacturer's setting marks.
A worn timing chain will almost always jump out of time right when the engine is shut off. This will suddenly create a "no start" condition the next time you try to start it; despite the fact that the engine worked fine the last time it was running. And that sudden, unexplicable change is what baffles many mechanics. But the key that gives it away is that the ignition timing usually changes by one cylinder position in the firing order. NOTHING ELSE WILL CAUSE THE IGNITION TIMING TO SHIFT LIKE THAT.
It sounds exactly like this is what has happened to your engine. And that is why I recommended replacing the timing chain and sprockets. This problem has nothing to do with sensors. It is a mechanical problem which has taken place inside the engine. If your mechanic knows how to check the valve timing; he can confirm that it now is not where it is supposed to be. A compression test is an easier, but less direct way to get the same information.