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Hi and welcome. This may be the what is called the pnp switch or neutral safety switch which tells the transmission ecu what gear the car is in. I don't think it is a transmission issue certainly seems to be electronic. I think you have 2 different problems with the starting this could be a crank shaft sensor or an ignition switch both are common on the saab. I hope this helps you .
If you have any further questions please let me know.