Unless either your hardware or Tomcat are damaged, Tomcat alone, or Tomcat + admin webapps typically starts up in under 10 seconds.
You should be able to track the startup process in the stdout (catalina.out) file. You can try clearing out the TOMCAT_HOME/temp and TOMCAT_HOME/work directories to get rid of possibly-stale files before starting. I always do that when deploying a new version of a webapp.
On the other hand, one particularly ill-written app I once inherited took over 30 minutes to "start up Tomcat" because the fool that designed it attempted to load entire database tables into RAM on startup - in the
servlet init methods.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.