In some environments Zimbra doesn't always start by itself on reboot, even though it is supposed to.
If you can ssh into the server, become or log in as root, and then execute the following:
If Zimbra is running, you'll see something like this:
viognier:~ # su - zimbra
zimbra@viognier:~> zmcontrol status
If it's not running, execute the following:
Post the results and let us know how things turn out!
zimbra@viognier:~> zmcontrol start; zmcontrol status
Hope that helps,