Tomcat itself is not an EXE. It's a JAR that runs via the "java" command of a JDK JVM. The EXE and service stuff is wrapper code specific to Windows.
So if you are able to launch Tomcat OK from the "Tomcat.exe" command, then Tomcat itself is OK and you simply need to check the configuration in the Windows Service Manager or whatever cute name Microsoft has assigned it for the release of Windows you are using.
The main things you need to check are that A) the service manager knows where the Tomcat Windows Service executable is and B) the start option (manual, auto, etc.)
Also don't forget that like all networking apps, only one process can listen on a set of TCP/IP ports at a time. So make sure that no other copies of Tomcat are already running or one of them will have grabbed ports 8080, 8005, 8009 and 8443 and prevented the service from using them.
When it comes to destroying a civilization, gas chambers cannot hold a candle to echo chambers.