ORIGINAL: Christoff
This is either an electrical fault or a mechanical one. If its electrical then could be the mentioned relay. Although not knowing about these cars in particular i could be wrong.
Mechanical fault though, has it been smoking much? Leaking valve stem oil seals?
High amounts of oil in the combustion chambers could cause hot spots around the plug and cause the engine to run on without ignition.
not without a fuel supply it can't .[

] the Motronic fuel injection system has various safety features built in to prevent the car catching fire if involved in an accident . Without the DME relay activated the fuel pump can't pump.
Something is preventing power being disconected to the ECU and the DME relay is staying energised supplying power to the fuel pump and ignition system.
As Rob says pound to a penny its a faulty ignition switch. Have you tried wiggling the key when switching off ?
Be careful when fiddling with the wiring to the switch as there are constant live feeds direct from the battery which can only be disconnected by removing a terminal at the battery.
I would leave one battery terminal loose for quick removal in case you have a short. Don't worry about your battery being disconnected as the engine management (ECU) has a non volatile PROM which retains all data in event of a loss of power.
I'd look at the immobiliser as wellit could be providing an indirect 12v+ to the DME relay.
For now you could pull the DME relay which will shut off the supply to the fuel pump and ECU but it won't take too much of that without failing.
Better to use a 3xway bypass with a switch built into the 3xway bypass wire from terminal 30 of the DME relay socket.