I am trying to find the cause and hopefully a simple solution to the following problem. (This is a description of action and following effect.)
Start engine with transmission in P
Shift into D4: green "S" light comes on. At this point the light is on only in the D4 position of the shifter.

 

S for Sport

 

I guesed you tried to depress the sport button? Does your speedometer work?, if not, it could be the speed sensor.