I'm not 100% sure if yahoo chat uses java (though I THINK it might). If it does, that's probably the problem.
There was a big and boring legal dispute between sun microsystems, and Microsoft. Microsoft lost, an therefor do not now offer the "Microsoft" VM (even though sun made it., which enables IE6 or better to support java environments.
Instead, browse to Sun Microsystems site, and download the latest J2RE (Java 2 Runtime Environment) Install it, reboot, and try again. All things java should then work.