Engine Mechanical problem
1997 Mitsubishi Eclipse 4 cyl Front Wheel Drive Manual 111000 miles

When I go to Start my car up in the morning, it startes fine. Everything Runs Great! Then after I shut it down and go to start it up again when it is warm. It will turn over but wont start, then if i shut the ignition off and try to start it again sometimes it will start and some times it wont and I have to repeat the process or let it cool down and then it usually starts. The Check Engine Light Came On When This Occured.
Thanks Kc

Check the fuel pressure confirm that its within specifications and comeback with the readings . Or you can try below and determine if its a fuel or spark issue when it refuses to start

Get a carb cleaner and spray into the carb or the throttle body on an EFI. Did it start and die? If not disconnect a sparkplug wire or 2 and ground it to the engine -have helper crank engine over-do you have a snapping blue spark? If so-you have a fuel related problem, check the fuel pressure to rule out the fuel filter/fuel pump/pressure regulator and listen to the injector/s are they pulsing or hook up a noid light. No snapping blue spark continue to troubleshoot the ignition system-power input to the coil/coil packs,distributor pick-up coil, ignition control module, cam and crank sensors- Note: If it doesn't apply disregard it

Error Code p0352 It says that my coil is going bad... Replaced Coil Still same problem somtimes it starts somtimes it dosnt. I also got some electrical cleaner and cleaned the connector on the coil and the two connectors on the Computer it self..

Get the computer scanned for OBD2 code/s Autozone will do it for free and get back. Also have you checked the fuel pressure? Also test the ASD relay if it has one-

Well I hunted down the ASD Relay and pulled the plug out and it was all gunked up, took some electrical cleaner and spryed it on it. Hasnt repeated the problem yet. I read somewhere that the engine light will go out after 40 or so successful starts is that true?

I read somewhere that the engine light will go out after 40 or so successful starts is that true? Yes the computer is relearning itself-40 key starts or more-