How did you install Tomcat?
If you used the .exe version and want to have the start menu items or if you were running Tomcat as a Windows Service; and wish to do the same on the new machine, you'll want to install a new copy there.
If you're just starting it from the command line and want to do the same on your other machine, you should be able to copy the whole Tomcat directory.
You'll need to make sure you have
Java and that your JAVA_HOME environment variable is correct on that machine.