Replaced ignition control module on 2001 saturn l200 2.2 litre engine and now car won't start

You mentioned at least six parts you replaced,
at some expense & I assume no testing at all

Now I suggest, you have a repair shop properly
diagnose the issues & resolve

If I crank the motor while it is st ??????? Probably ignition module . When it shuts off check for spark .

Someone would need to check for power and ground at the coils and that the timing belt is ok.

For car running hot and overheating issues, I suggest to you go through this help links. Click this link below and go through the troubleshooting procedure to take care of the problems: ----Car runs hot? http://howtobyme.blogspot.com/2011/11/car-runs-hot-in-traffic.html
-----------All types of car overheating problems and troubleshooting?

http://technoanswers.blogspot.com/2011/11/all-types-of-car-overheating-problems.html
Car freeze overnight and started overheating while driving?http://technoanswers.blogspot.com/2012/01/car-freeze-overnight-and-started.html-----------Engine Overheats and heater blowing cold?

http://howtobyme.blogspot.com/2011/11/engine-overheats-and-heater-blowing.html

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Car overheats and Air blows hot at idle?
http://howtobyme.blogspot.com/2011/11/car-overheats-and-air-blows-hot-at-idle.html
--------overheating? http://schematicsdiagram.blogspot.com/2011/12/buick-century-overheating.html
----------Car engine Overheats and transmission starts slipping?http://schematicsdiagram.blogspot.com/2011/12/car-engine-overheats-and-transmission.html
----------This details will help.Thanks.

Done cars have a kill switch if they are low on oil. Check your oil. If the oil is good, it may be the ignition switch.

If the engine fires up for a second or two with starting fluid then the fuel pump is weak.I would check the fuel pressure and if its not within the specs then replace the pump and filter.

Check the coils that have been replace for bent or broken prongs that plug into the ignition control module and if nothing looks damaged then i would think the ignition control module is faulty.Replace ignition control module.

Sound to me your crank sensor has failed.The only solution is to have it replaced.

you may have a failed ignition lock cylinder, the only for sure way to know is to take the car to a gm dealer and have them diag the car. (read the code) You can not bypass the theft system it controls fuel and ignition control module. If you have an independent repair shop with a scanner that can read a saturn control module it might be cheaper. The parts you will need tor replace isa lock cylinder new key and have the new lock cylinder coded

What Dealership ?????? Saturn dealers are no more . What is it you would like to know ? Complex electronic's involved . Ignition switch is low voltage input to the BCM - body control module. Have seen this problem your having before , BCM problem ! Service engine light on ????? What DTC'S - diagnostic trouble code's are stored , same for air bags an Traction control "OFF" What code's . Any code's stored in any module ? Do a full vehicle scan .

The body control system consists of the body control module (BCM), communications, and various input and outputs. Some inputs, outputs and messages require other modules to interact with the BCM. The BCM also has discrete input and output terminals to control the vehicle body functions. The BCM is wired to the GMLAN High speed serial data buss and the GMLAN Low speed serial data buss and acts as a gateway between them. If the BCM does not communicate the vehicle will not start due to the inability of the engine/powertrain control module (ECM/PCM) and vehicle theft deterrent (VTD) control module to communicate without the BCM providing the gateway function.

Power Mode Master
This vehicles BCM functions as the power mode master (PMM). The ignition switch is a low current switch with multiple discrete ignition switch signals to the PMM for determination the power mode that will be sent over the serial data circuits to the other modules that need this information, and so the PMM will activate relays and other direct outputs of the PMM as needed. Refer to Power Mode Description and Operation for a complete description of power mode functions.

Your best bet , try a different dealer .