I was having significant difficulty with Local’s router failing to start after upgrading to 5.2.3, same issues with attempting to bind to port 80 while currently in use. After doing some research, I found this article, which was incredibly helpful: http://www.devside.net/wamp-server/opening-up-port-80-f
Turns out the BranchCache Windows service was hogging port 80 to itself in my case. Disabling the service fixed the issue.