1) ok, to Which Linux distribution is Zimbra installed ? RHEL, SuSe, ...
2) Have you recently connected via web browser to your Zimbra server on the admin network port, 7071? This is a useful tool - the admin console. Similar to a URL of https:/host.domain.com:7071. Then logged in with username similar to
admin@host.domain.com # look for the server status which is the inital screen. copy what you see into this forum thread please.
3) Please perform /etc/init.d/zimbra restart # something is not correct, and a reset might help put useful messages in log files often in /var/log/zimbra.log in an easy to find location of the file.