I had the exact same problem. Chevy Aveo 2004, 4'th gear won't shift, same error codes.

As I could not find an answer anywhere, I write here the solution (at least in my case), in an attempt help the next measurable guy. After more than a month of countless false attempts, it turned out that the problem was in the timing belt. It "jumped" two teeth away from its right position, in one of the camshafts sprockets.

The problem was just a weakening of the "automatic stretcher" of the timing (aka spring). Re-aligning the timing belt to its right place will not solve the problem as in the next steep hill it will jump again. The timing belt mechanism, especially the stretcher, must be replaced with a new one.

Pay attention aveo owners: (In my experience) the timing belt mechanism in chevy aveo (2004) is amazingly, unbelievably, poorly designed and poorly constructed. It’s a huge weak spot that could ruin perfectly good-condition engine. Frequent checks are recommended.