2011 Jeep Grand Cherokee Start problem

Dear, my 2011 Grand Cherokee Laredo (VIS 1J4RR4GG9BC709626) has an intermittent starting problem. It is not always, but happened 4 times in the last 30 days. Basically, it doesn´t start at the first try, it cranks and cranks but doesn't start. Then I just press the start button (switching off and on ) without pressing the brake pedal. After that, I press the brake pedal and the start button and the car starts right up normally. It looks like the car is out of gasoline, but for sure it isn´t. I took the car to a Jeep Garage and they said I must change an engine module (part # is 05150656AA) that cost around USD 2.5 k here in Brazil. Too expensive! However, it sounds they don´t know what is actually the reason of the problem and just want to sell me an expensive part to make money. I would appreciate if you could help me? Thank you very much!