4L60E won't shift.
Was the PCM or tune changed? Give us more history of recent changes to your car, especially what has been changed since it last worked. If this is a new car for you, get it tuned properly as it sounds like somone hacked the tune.
A bad MAF, TPS or MAP sensor might also give you those symptoms. A good scanner can verify that each sensor is sending valid data to the PCM. Once all sensors (also VSS) are verified, use a scanner to command each trans gear and verify that it shifts. This can be done with the rear wheels in the air and a good scanner, or have a trans shop do it for you. There is likely nothing wrong with your trans; just an engine sensor or the tune.
Sorry I cannot recommend a specific scanner for you because I, like many others here, use the very expensive HP Tuners or EFI Live which runs from a laptop.





