I need to turn my key two or three times to engage the starter most of the time.

What is your question?

Auto Trans, 141000 miles. New starter last year, new battery last year. Lately, most times but not all the time, I need to turn the key multiple times to engage the starter. There is power present to the accessories but not the starter. Could it be a battery terminal or is it likely to be some electrical switch in the trans selector or ignition switch?