Did you verify the suspect solenoid was really electrically and mechanically  DOA, with a bench test and still not  an unresolved harness concern. Did you verify all prerequisites required for the relearn to take place without the test aborting or failing have been met , like the required  transmission fluid temperature range and no pending codes,etc? 

  Did you try an auto scan and quick erase of all the modules in the vehicle to see if there are other system codes and possibly resets that may need to be performed like for steering angle sensor and yaw sensor if equipped with VSC and traction control, or even tire size may need to be entered ?

 Any luck on carrying out relearn procedure?

 there has to be a trouble code still stored in memory for that light to keep coming on or flashing. try a hard reset by disconnecting both battery terminals and touch them together, that should clear caps and reset codes. recheck for any pending codes, a relearn is not possible with a pending code. if the vehicle drives fine and shifts through all the gears with no trouble codes, I will suspect a bad tcm. usually a bad solenoid either shuts down the driver in the tcm or fries it. a relearn can also be perform by driving the vehicle for a few miles.