I ran across a very similar problem. Assuming you're using Java Plug-in 1.31.1, just go to your control panel. From there select "Java Plug-In 1.31....". When you get to this Java Plug-in control panel, on the "Browser" tab, there should be check boxes which enable Java 1.3.1 as the default Java runtime on IE and Netscape. De-select BOTH. Apply these changes and you should be good to go.

Once you go back to Yahoo chat, it'll use IE to load the applet rather than Java runtime. I'm not sure why this setting defaults to "yes", but that is all it should take to correct it.