Same here with G5/10.4.8/
Mac OS X comes with a Sun JVM by default, either 1.4 or 1.5, depending on your OS X version and Mac hardware platform, i.e. PPC or Intel. Unless someone does some major open-lib surgery, the Sun JVM is there to stay. The only thing you could try is to see (and possibly switch) the standard JVM version with the Java Preferences tool at /Applications/Utilities/Java/J2SE 5.0/Java Preferences. Most Mac users on a recent version of 10.4 will have done the J2SE 5.0 update by now but may have changed their default JVM for some reason.
And to follow up on the actual error, I have the exact same problem with a dual 2.0 G5, Mac OS X 10.4.8, JRE 5. The Zimbra Desktop icon pops up a link to http://localhost:7633/zimbra/mail which for me too renders:
HTTP ERROR: 404
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Incidentally, and as an aside, the Windows version most likely comes with a JVM because MS never bothered to include a proper one with their OS, which makes one of the first orders of business with any new Wintel machine a download and install of Sun's JVM. But again, that's entirely OT. ;)