You should never be manually starting any service other than the CiscoWorks Daemon Management service. The other services (except RCP, TFTP, and syslog) should be set to manual, and you should never use the Services control panel to do anything with CiscoWorks services unless directed to do so by TAC.
If Tomcat will not start, check NMSROOT\MDC\tomcat\logs\stdout.log, and see if there are any errors there. If this log is not being updated, the the Tomcat VM may not be getting properly initialized. Make sure you have at least 2 GB of physical RAM in the box and 4 GB of swap space. If you do, and Tomcat still will not start, double the swap space and try again.
If, after that, Tomcat will not start, open a TAC service request as you will need to do some additional in-depth troubleshooting for this problem.