'89 Escort troubles

My mothers Escort has had the check-engine light come on a couple of times inexplicably, and then go out after the car sat for a little while. I've tried using a code reader to find out what's up, but the ECU hasn't stored any diagnostic codes. Is that just an OBD2 thing, or should hers do it too? This might be unrelated, but when she starts the car in the morning it runs for a few seconds and then abruptly dies, after cranking for a maybe 5 seconds (strong cranking, new starter and newi-sh battery) it finally restarts.

Does anyone have any insight on these? My first thought for the check-engine light was that maybe a sensor was getting wet, but it's been fairly dry (for Seattle) lately.

Mine recently started doing the same thing... comes on for 5-10 seconds and goes away. I suspect a sensor has gone bad or a wire is loose somewhere but have not yet got the code reader on it to check it out.
Check the connectors at the crank and cam sensors, make sure the air filter and pcv valve are good, and if you have a vacuum tester check your EGR valve. If it all checks out good, I would chalk the problem up to old age (the car) and not sweat it.... so long as the light does not stay on.

It could be a fuel delivery problem. Instead of cranking it for 5 seconds try turning on the key to run several times before you crank it. You should hear the fuel pump running each time. This will bring the pressure up in the system if that is the problem and you won't be wearing the starter out not to mention the battery.