Welcome to the forums,
You should be able to work offline regardless of plus or free account type - there's no restriction on anything.
Is this "can't connect to server" when you try to bring up the webapp? Is the background service running? (Prism
should now start the service if it's not currently running, but it seems something isn't working properly on your system / or you're trying with another web-browser on localhost:7633)
Can you check the zdesktop/log/mailbox.log? (so on your platform XP that's drive:\zimbra\zdesktop\log\mailbox.log)
Let's make sure the service is started (or restart it):
Windows key + r > run > services.msc > Zimbra Desktop
Troubleshooting : Zimbra Desktop - Zimbra :: Wiki