The security systems don't operate like they used to on older vehicles. On older vehicles they would shut off the fuel injectors
On your vehicle, the security system(sentry key immobilizer system) works differently. It sends the security status to the PCM and when the PCM doesn't receive a valid key message, it will allow the vehicle to start and stall three times and then shutdown the starter control until it sees a valid message. So basically if the security system was the problem, it the security light would either be on solid or flash.
Most of these problems are caused by a fuel supply issue or an injector problem, but without being able to check the common rail pressure, it's impossible to say.
If I were to guess, I would say this is a fuel issue or an ECM issue. I thought you might have a cracked #4 injector line, but if there is no leak, then that can't be the problem. These are very bad for cracking the #4 injector line and it will not start when that happens.
I sure wish I could do more, but when you have a problem like this, it is very difficult to diagnose without a scan tool.
If you have any other questions feel free!