The turbo will spin whenever the engine is running. It doesn't "engage" like a gear, it just spools faster as exhaust flow increases.

There are two possibilities. One is that there is some problem with the wastegate. I believe your model has a pressure operated wastegate, which is usually pretty foolproof. But the gate itself can become rusted in place. Often this can be repaired without removing the turbo by unclipping the actuator, spraying oil on the pivot, and working it free by hand.

But the more likely (usual) problem is that the pressure sense line or the switchover for the ALDA has become clogged. You can find a photo how-to here:

dieselgiant (DOT) com/mercedesaldaboostsystemservi.htm