Real car question...

I have had a problem with my 86 Celica for about 3 months now. Keep in mind that the battery has tested good and the connections have been cleaned. The starter is new as of 6 months ago and the alternator is new as of one month ago. The car starts hard in the morning or after 3 or 4 hours of last use. Within a few hours, it starts right up again. In the morning, I have to crank it at least 4 times to get it to start. Then it barely idles for about 10 seconds with the engine light on before it kicks in to normal rpms and the engine light goes off.
I have heard many theories but none of them make sense because of the fact that it starts right up if it is still relatively warm. The only 2 I have heard and I don't know about is a bad cylinder ring and the O2 sensor.
If anybody has any thoughts on this, it would be appreciated.
Don't hesitate to respond to me directly.
Thanks, Jim
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