Most likely the GPS unit was just a coincidence. It is very common for the Navigatioin units to go bad on this year.
For the starter, I think I have the correct wiring diagram.
The starter control goes through an EWS module. This module is there for theft protection. It has to see a valid key and then the code checked from the DME (engine module) to allow the starter to turn. There is a relay also that could be the problem.
The starter relay location is: In the Ebox with the DME and EGS module. This would be in the engine compartment on the passenger side under a plastic cover.
rear RH side of engine compartment in E-Box under control modules
The first thing to check is do you have voltage to pin 6 at the relay when cranking. If not then the EWS is most likely the failure.
By looking at the relay wiring if 12 volts were applied at pin 2 the starter should spin. This would be in essence jumpering the starter from the relay like you are doing with a screw driver. If the starter turns from this point it shows that the wiring is good from the relay to the starter and again points to the EWS as a possible problem. I would also try another key as a bad key could prevent the start signal from being release from the EWS module.
I hope this information will be helpful. Thank you.