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I have been a professional master mechanic for over 35 years and am happy to help you with this.
Two possibilities are the starter relay and the park/neutral safety switch on the top of the transmission.
the starter relay is located in the fuse box under the hood, passenger side.
When someone else is trying to start it, hold your finger on the relay and see if you can feel it click. Its supposed to click. Of course this has to be done at the time it wont start. If you can feel it click i would replace the neutral safety switch.