2005 350Z will not start sometimes

2005 350zwill not start sometimes. Took the car to the dealer and they checked itover. Dealer hooked up fuel pressure guage, no problem found. Checked spark, battery, ignition, nothing. Dealer suspects interference between the key (chip) and ignition. He asked that my daughter remove everything from the keychain excep the the key and fob. THis worked for about 1 week with no problems starting the car. Then one morning my daughter tries to start the car, nothing. It was cool maybe in the mid-40s. It started fine later in the day. The dealer offered to come to the car when it woould not start to debug onsite. Nice, but it now starts everytime. Maybe it has something to do lower temperature? Choke, but its fule injected? Thoughts.

When You Turn The Key And It Won’t Start, Does It “Click” Or Does It Crank The Engine Over, But Not Fire-Up, Or Does It Do Nothing At All, Not Even A Click ? Describe, Please.

CSA

Does not click, it just cranks and engine does not fire. After trying once or twice I can retrun in a few hours and it cranks over and starts.