1997 Mitsubishi Eclipse Starting Problem

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

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-

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-