Thank you for giving me the good direction.
As I am on Windows 64 bit, I had the JDK in 64 bit. I found the good version and installed it.
Plus the Tomcat Installer set up itself on 64 bit automatically, so I used the zip version.
Finally, at the start up attempt I saw a wrong version of JRE being used, I had to do a set JRE_HOME=C:\Program Files (x86)\Java\jre6.
It was not that difficult, but I needed a tip. Thanks!