Do you have Fuel Pressure? Because I've gotten a few faulty fuel pumps from aftermarket companys and even through mopar. Check the Fuel pressure but a Crankshaft Position Sensor is a common thing to go on those. they dont normally work intermittenly Maybe they are two sperate problems but before replacing the sensor check your fuel pressure.

There are many things that can cause that problem. What you know is that your battery and starter solenoid work. When it cranks, does it crank normal speed or is it slow and labored? If the engine has gotten "tight" after overheating, it may not get going fast enough to catch. The next question is fuel. Why did the fuel pump burn out in the first place? Did you replace your fuel filters? Could they be so plugged that gas can't get through them? Is there gas in the tank? Do you have a leak in the tank or lines somewhere? If you have fuel, so you have a spark? Is your coil working? Are the coil wire or spark plug wires deteriorated to the point where the spark is escaping the insulation and getting to ground through the block or frame instead of through the spark plugs? Are the spark plugs themselves in working order. If you have ascertained that you have fuel and spark, the next question is compression. The gas/air mixture has to be compressed in order to explode and push the piston down. This has to be checked with a special guage, so take it to the dealer for this test. If your rings are gone, you won't get compression and power, you'll get blowby into the oilpan. Often when this happens, you'll see the dipstick popped up a little each time you check it. Those are the issues that haven't changed since before sensors and in my experience, they are more likely to be the actual problem than the sensors that monitor them and that we all replace when the car stops running. The sensors are useful for making the car run efficiently, but I've found they aren't really useful when it comes to diagnosis.