Check your Security firewall. Sometime it will not allow to run the applications. Is there is any error while installing the tomcat. I recommend you to install tomcat using window Installer (.exe file) for tomcat.
Its not disappearing. I guess Classpath is not set(CATALINA_HOME , JAVA_HOME) . Read the installation that comes with Tomcat. If you want to know the exact error open your command prompt and run the startup batch file from command prompt.
JAVA_HOME Must point at your Java Development Kit installation. CATALINA_HOME MUSET POINT UR TOMCAT DIR
U CAN PUT THESE ENV VARIANLE IN AUTOEXCE.BAT AT C:\ OR CAN SET THE EVN VARIABLE as
RIGHT CLICK ON MYCOMPUTER & SELECT PROPERTY THEN SELECT ADVANCE TAB & CLICK ON Environment Variable you will see the tow type of variable System variable & user variable
click on new at Variable Name right CATALINA_HOME at Variable Value right (path where u have installed tomact4.1) again click on new at Variable Name right JAVA_HOME at Variable Value right (path where u have installed jdk1.4)