The Apache error log doesn't display anything helpful. I used the 'Test Port 80' option on the WAMP menu and it says that yes, Server: Apache/2.2.21 (Win32) PHP/5.3.10 is listening on port 80. However, going to localhost results in a connection refused message.
I disabled IIS, restarted, started WAMP and the icon turned green. Turns out Windows had installed and ran IIS automatically (why?). Upgraded to Windows 10 today and had an orange WAMP icon on my taskbar. I had WAMP working happily on windows 7 as my local development server.