can a 2002 2.4 regular engine be replaced by a turbo of the same year?

You have to swap the ECM and maybe the BCM from the turbo car.

I did not swap the turbo parts. I am trying to use just the basic engine without the turbo. I was told by the engine suoolier that it would work, but so far, I can't get it to work.

Did you just swap the just the engines or did you reuse all of the upper end stuff off of the old engine on the turbo one? They are completely different engines from the head up.