As everything else is working, you are probably suffering from one of four faults.
1. A imobalisor gone bad.
2. A bad starter motor.
3. A bad ignition switch.
4. A bad gearbox (tranny) inhibitor switch.
To test if the starter motor is O.K. there is a three pin plug against the firewall which if you unplug it and bridge the middle pin with the battery positive, will cause the starter motor to engage.
I have attached a pic of my W126. I know it's completely different, but it's just to show where abouts the plug is situated on your car. Where I have circled in red, the plug is on the inside of the firewall at that location. It is on this side on UK right hand drive models but not sure on left hand drive, so check both sides.
If the starter engaes then you have ruled out a bad starter motor.