2001 Saturn L300 Engine stalls out

First of all thank u so much for ur donation it really helps to keep us going and answering everyones questions. Ur p1780 is a request from the transmiision to turn ur service engine soon light on. Ur code p0727 is engine spped circuit no signal. Niether code has anything to running out of gas what I think is going on is u have a bad crank shaft sensor. It gets hot stops putting out a signal and ur car stalls till it cools down. Heres what u need to do if u have a multimeter if u dont have one u need to get one that reads ohms. Find ur crank sensor its right next to ur oil filter housing it has a wire attached to it that has a tin foil looking tube around it only one looks like it. Follow the wire up under the hood to wire it plugs into ur engine harness. Now run the car till it dies and wont start then unplug the crank sensor. Now take ur multimeter put it on 2k setting take ur two wires from the meter and put them on the two wires comming off ur crank sensor. If its bad u should get no ohm reading it should read as a open. If not let me know what it reads.

I was going by the fact u told me that the car was a L300 that only came with a v6 and my test was for a v6. So when the car died and would restart u tested the crank sensor end of that wire not the engine harness side?Also u checked it for ohms value?What ohms value did u have?If the ringing noise was under the hood that was just ur throttle motor that's normal. That two clicks was ur throttle motor doing it's self learn for idle it does it anytime it sits with the key on and not running for over a min normal. Let me know what those reading are.