1989 Chevy Cavalier car wont start after turned off

When the vehicle refuses to stsrt, If there is no sprak at the plugs and no injector pulse, my first thought would be the crank sensor. It could also be a problem with the ignition module, can't be sure, from here. The crank sensor might be around 20 bucks, sometimes it is a son--of--a--gun to remove. The ignition module might be around a hundred bucks. I'd try to some testing before I replaced anything.

How good are you at, checking under the hood? When the vehicle refuses to start, pull a plugwire off plug, stick a known good plug in the boot, lay metal part of plug to metal part of engine, have helper crank the engine, watch for spark at the tip of plug. Also, the autostores sell cheap spark testers, you can use one of those instead of spark plug, whatever.

Is the car cranking over but no start or is it turning over to slow to start. Kinda acting like it has low battery?If its the later answer you have a starter that is getting worn out. Its called heat soaked.Parts stores sell blankets that wrap around the starter to keep it from getting to hot and prolong the life.there about 30 bucks.If thats not the issue follow the steps from the other poster.