Re: throtttle cable adjustment
Was the lever hard to push before you replaced the key switch? If not, then it is possible somthing is binding in the control box because you reassembled it improperly. Most control boxes have a knob for controlling lever tension. Find it and back off the tension a little. The lever has to have some play when moving from neutral to allow it to shift into gear before revving the motor above idle. Ensure the cable does not have short radius bends, which may cause it to bind.
"is there a possibility that the conectiions on the motor end have worn out?" Not sure what you are asking there. Does it appear to have wear?
When I first put my boat into the water this year, I noticed that the control was stiff and slow to respond for both speeding up and slowing down. Turns out the grease at the pivot for the engine's throttle lever (on the side of the engine) had dried up causing binding. After cleaning and relubing the pivot ...... much better.