Saab wont start will turn over but it will not start could it be computer?

If the starting problem only happens in the Summer when it is really hot and after a short drive when the engine is hot, it is an overheated neutral safety switch. Many were defective and if you replace it from a junk yard, you can get another bad one.

Try this. Keep a container of water in your car. When the car does not crank, squirt water on the NSS to cool it off. It looks like a base that the battery is resting on ( in my 2001 9-3). When it is cool, the car will start. Really.