My Infiniti Q70 will start then turn off, I doesn't happen everytime. I changed

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My 2014 Infiniti Q70 will start then turn right off, it doesn't happen every time. I had the battery tested they said I had a bad cell so I changed the battery. The very next day it started happening again. Today it did it 4 times before I could get the car to remain started. I took it to the auto store everything is reading in good standing, they don;t know hwy it's happening. and of course it didn't happen while they tested it. I did some research it could be a lot of things. How possible is it to be the brake light switch under the dash?? Please help, I'm trying not to end up at the dealer with a bill I can't afford!

How long has your 2014 INFINITI Q70 had this problem?

A few weeks