If the vehicle cranks, I'd bet the ECM is ok since it controls the starter relay, and I've never seen a whole bunch of problems with the computers the LeSabre's.
I would probably start off by doing some basic checks, since you know it cranks ok. Two basics you should get out of the way first would be to check for spark and to check fuel pressure. You can either remove a spark plug
wire from the coil or plug itself and check spark there while someone cranks the car over. If you have spark, you can assume that you have a good ignition module and crank sensor.
A fuel pressure check can be taken right off the fuel rail if you have a gauge. It should be at least 48-55psi with the key on and hold steady. If it less than 45psi or the pressure drops off right away, you probably have a bad fuel pump. Also, check the fuel pressure regulator for leaks too if the pressure drops off, but that won't usually cause a no start condition.
You might also want to just verify there are no trouble codes set by doing a scan one more time. You don't want to overlook anything. If both the spark and fuel check out, then you could be looking at a wiring problem, a sensor that is shorted out, or lastly and least likely a bad ECM.