We had a newly updated Exchange 2013 SP1 that would not start the Transport service
"Netstat -b" showed that a service was listening to port 25 on all IP's (0.0.0.0:25) and when the service could not get the port, it would die, and Exchange would attempt to restart it over and over.
After many tears, I found this solution:
Through the console or the ECP, check the Frontend receive connectors and find the one that is listening on 0.0.0.0:25, which is probably the Default Frontend Receive. Disable it.
Restart the MSExchangeTransport and MSExchangeTransportFrontEnd services.
If both services restart normally, troubleshooting is complete.
We use several custom connectors carried forward from the previous installation, which was SBS 2008. If this applies to you, take notice.