Macbook pro not booting after travel

I have a 2013 13 inch macbook pro. I closed the lid shut when there were programs running, put it in the carrying case and went to the airport. I was at the airport in less than an hour. At the security desk when I took out the macbook it wasn't noticeably hot. I put it back in the case and after takeoff I took it out of the case to work. It wouldn't boot. All I see is a grey screen and the computer is slightly hot at the bottom and back. I have tried many times since then to reboot with no luck. I have tried holding the shift key after powering, holding command, option, P, R keys etc. Nothing. No sound. No logo nothing. Only grey screen. Is it kaput?