Essentially this is an exercise of divide and conquer. Obviously a working shifter will move if its not obstructed, you 'just' need to find the obstruction.
First and simple check is remove the wheel. Check the derailleur moves freely using the shifter, if it moves, the problem is related to the cassette and chain. Are you turning the wheel while you move the derailleur? If so, as suggested in comments, the H and L screws might be set to lock it.
If it does not move with the wheel removed, you want to check if the problem is cable and/or shifter related, or the derailleur itself. Undo the cable - you can often do this adequately by removing one of the outers ends from a stop. If the cable is free and the derailleur moves, the problem is in the shifter.
With the cable loose, check its free to move. Any stiffness gets amplified when pressure comes on the cable, lubing may help, but new cables are often the fix required, especially if its the cause of a derailleur not moving (usually poor cables result in poor shifting long before it gets this bad)