The first suggestion I can give is to be patient. No one is paying the staff to monitor this website 24x7, everyone here is a volunteer. So we check in when it's convenient.
This is your ultimate error:
And a NoSuchMethod Error is typically thrown when you have a loss of syncronization between 2 software components.
The getSessionCookieConfig method did not exist for the ServletContext class until
JEE Servlet spec version 3.0. So somehow, you apparently got a chunk of some older webapp server code mixed into your Tomcat 7 environment.
Remove any installed webapps and see if Tomcat will start. If it doesn't, then your Tomcat server is corrupt (or you may be very short on memory or disk space) and the quickest way to repair that is to install a fresh copy of Tomcat. If it does, then there's something wrong with one of your webapps.
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.