I recently took my car to the dealership to have.

I recently took my car to the dealership to have a diagnostic test ran due to my cars performance and the check engine and traction control lights coming on. Once they inspected it the said that the third cylinder didn't have enough pressure. And they suggested that I have the entire engine replaced. As you know, this is not cheap. So I'm hoping to find a way around this.
I've done some online research and seen a few posts from other Cobalt owners that are having the same problems I am. The check engine light stays on, the car is idling extremely low (and will occasionally cut off if the weather conditions are colder), the traction control light comes on, and when switching from first to second gear (not every time) it will sometimes jerk (my car is an automatic). No-one has really been able to pinpoint the problem. But one of the Cobalt owners said that they had their body control module replaced and that seemed to do the trick.
I was wondering if the BCM could cause all of those problems. Its my understanding that the BCM actually controls the lights and such. But the powertrain control module handles transmission, charging system, communications, and everything else. Essentially my question is, if by replacing the BCM or the PCM, could that possible make a difference in my cars performance?