It depends on which way it is dying.
Won't Disengage. This one is easy. When you come to a stop, the car shudders like a manual with the clutch still engaged. It stalls whenever you try to put it into gear.
Won't Engage. This one is tougher. At about 40 mph, you will hear the engine note drop a bit and the RPM will go down by about 200 rpm. It is sort of like a real subtle 4th gear. Orge's test is to cruise at a constant speed and lightly tap the brake pedal. An increase in engine RPM signals that the TCC just unlocked.
Of the two, not disengaging seems to be more common, but that may be just because it is more noticable.
