I have the same problem. I have tried uninstalling and reinstalling, but it doesn't work. This didn't really start until I added Tomcat. I can start MySQL and Tomcat, but the Apache does exactly what you said....it says it is started, but it never shows up as running, while the other two do. This is the only thing that shows up in the error log.
(OS 10048)Only one usage of each socket address (protocol/network address/port) is normally permitted. : make_sock: could not bind to address 0.0.0.0:443
no listening sockets available, shutting down
Unable to open logs