CRAFTSMAN, Model No. 917275751 is the correct model, made a mistake the other day, lubed the cable with no change, also note there is a grey switch under the engage lever, may be this switch is bad, however if the lever is engaged the mower will not start but if disengaged mower starts but then after engaging lever mower does not engage deck. How do I test this switch and what is it called.

The grey switch is the safety switch for the blades. Check your belts, check to make sure nothing is holding the blades and they will turn by hand with the unit off and the spark plug is disconnected, or the battery is disconnected.