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DI is the Direct Ignition cassette at the top of the engine. If one coil has broken then that would cause the problem you describe. Very simple to change, just four screw and a connector.
CEL is the Check Engine Light on the dash. If there's a problem the ECU knows about then the CEL should show up. Connecting the car to a computer (Saab use a handheld one called Tech II) should be able to read any fault codes to find out what the problem might be.
Another possible culprit is the CPS (Crankshaft Position Sensor). It tells the ECU where the engine is in its rotation. If that fails you can get poor running until it fails completely and then the engine will just turn over. The ECU doesn't get a signal so it doesn't know the engine is turning. A bit fiddly to change as it sits at the front of the block behind the exhaust manifold (held in by a single T25 screw). I changed mine last year in approx 20 minutes.
When you crank the engine does the rev-counter show anything at all? If it does 'twitch' a little bit then the CPS might be OK. If there's nothing then the CPS is likely to have broken. If you have a multimeter you can check for resistance between pins 1 and 2 on the connector. It's the blue one to the right hand side of the throttle body (looking from the front). It should be 860 Ohms +/-90. Sometimes when they fail they are much higher than that (up to 1,500 Ohms).
It could also be something simple like an air leak. Check the various vacuum hoses for any splits or a loose connection.