Could also be a bad starter relay or a bad range sensor on the transmission.
Use a multimeter to see if there is 12v on terminals 85 and 86 of the relay when they key is held in the start position to rule out a bad starter. Jump the relay 30 to 87 to rule out the relay. Then you're left with some more difficult testing of the ignition switch and range sensor. You may be able to check the range sensor by trying to start in neutral instead of park.
If it's an automatic, it can be your neutral safety switch. (I think that's what jvanabra is refer to as range sensor?) It keeps the car from starting if it's not in neutral or park. when it doesn't work, the switch gets confused as to whether it's in gear or not. My convertible has had issues with this when it first comes out of winter storage. Fortunately, it settles out after driving and moving the shifter. Try working the shifter through the gears a bunch and see if you can get it to go. If it does, you've probably found your issue.
Yeah, NSS is a misnomer. That's not what it does. The range sensor is a range sensor because it "translates" the physical position of the shifter (and thus the transmission) into an electrical signal the TCM uses to know what gear has been selected. It senses the selected range. Saab repurposed the P and N ranges for the starter interlock, which in retrospect wasn't good idea... unless you wanna sell some range sensors, I guess. womp womp