Exchange 2013 ECP/OWA/Outlook all failing - 503 Service Unavailable
No thanks to the helpful down voters. The nice people at Experts Exchange helped out.
The solution was the SSL certificate seemed to have come off of the Exchange Backend website. Selected the Exchange certificate on the IIS site and it started working. for all the details please see http://www.experts-exchange.com/questions/28699498/Exchange-2013-ECP-OWA-Outlook-all-failing-503-Service-Unavailable.html
I also had very similar issues where after a reboot of the Windows Server my Exchange instance was installed on, I was encountering 503 errors on all web sites (OWA, ECP etc). After around 30 minutes of troubleshooting, I realised the system clock was off around 20 minutes. Just adding this here to hopefully save someone the frustration in the future!