You can use GROUP BY with HAVING as follows
Query
SELECT DeviceID FROM DevicesTable GROUP BY DeviceID HAVING SUM(CASE WHEN Transmission = 'Inventory' THEN 1 ELSE 0 END) > 1 AND SUM(CASE WHEN Transmission <> 'Inventory' THEN 1 ELSE 0 END) = 0
SQL Fiddle
OUTPUT
DeviceID 000329
If you want to check only Transmission in ('Starting','Stopping') , you can add Transmission in ('Starting','Stopping') instead of Transmission <> 'Inventory' in the second conditional aggregation.
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