1991 Acura Integra 1.8 Litre, miliage unknown

We have a 1991 Acura Integra, 1.8. It blew an engine so a replacement engine was installed so the mileage is unknown at this time.
The problem or problems:

When first starting and turning the ignition if the engine light stays on while going through the system check it won't start.

If the engine light goes out normally it will start.

After it finally starts it won't accelerate properly unless you "feather the accelerator" till it reaches 2000 rpms. If the engine is cold it will run properly until it gets warm then it won't accelerate.

The computer does not have a diagnostic lead for a diagnostic computer to be hooked up to it. The mechanic read the flashed on the eye on the vehicle computer. THEN the mechanic took it to a second mechanic for a second opinion and both agreed it was the distributor That was replaced. The problem still exist. Any suggestions would be appreciated. When it was idling today while I was there it sounded like it had a slight miss but other than that it ran good.

Teresa