Problem solved (check for correct rpm:s!)
Hi and thanks for your answers. I suspected that SE Linux might complicate things a little. However, the problem in my case was that OpenLDAP didnt run as it should (the Java Error mentioned earlier in this thread). OpenLDAP won't run if a rpm i missing, in my case libbind.so.3. Thanks to another thread in this forum, I solved this issue successfully and now Zimbra is running OK.
I can logon to the web interface for administration and I also tested the external authentication to my Windows 2003 Active Directory, it worked super!
A tip for all you how experience this trouble with Java communications error is to check the forum for information about how to install (AND UPDATE!) packages that OpenLDAP depends on.