This is a problem that has existed for me for quite some time... going all the way back to mozilla-0.9.9 as distributed with redhat 7.3. In all this time, I've never been able to get sun's java plugin to work for a regular user with mozilla (I've had success with galeon). I've tried both sun's jre 1.3.1_04 and jre 1.4.0_01. It just doesn't ever do anything for webpages with java applets (acts like there is no java plugin). Two oddities: 1. the plugin *is* displayed in mozilla's About->Plugin's menu. 2. the plugin *does* work, only if running as root.
Sounds like some sort of permissions problem. I've been using the java plugin here without problems for a long time.
The funny thing is that the java plugin works fine in Netscape4, konqueror, and galeon, just not mozilla. Which java runtime are you using, and where/how did you install it? (I have it installed to /usr/lib/sun-j2se1.3 and /usr/lib/sun-j2se1.4 repectively, with plugin symlinks into /usr/lib/mozilla/plugins).
OK, I'm a tard... it helps to actually have the "enable Java" preference activated... (-: