Hi, Minsk; Being that the dealer has exhausted their tests, not much left for me to go on. I'd put a fuel pressure gauge on it, let it sit over night, and see if it still has pressure or what the pressure is when you first turn on the ignition. Does it run rough for a few seconds when it does start? Could be a check valve in the pump or an injector leaking? I'm sure that they've checked the CTS? Try turning on the ignition (when cold), turn it off, wait a few seconds, turn it back on, then try starting. If it does start normally after cycling the ignition, you're headed in the right way. Each time you cycle the ignition, the fuel pump runs for a few secs. and builds pressure. Just a guess. That would point to the check valve in the pump or an injector leaking.
Good luck.