If it's a work machine, it is likely that the IT guys turned off all java functionality that is not needed for internal apps. That would screw up the applet. Or it might be a problem on Fyron's end... he does always seem to be mucking around with things
What you can do is install Trillian on a computer you have admin on, and with a CD burner. Once Trillian is installed, you should be able to burn the progam folder to a CD and run from that, or at least you could with 2.0 version. Or if you have a portable hard drive (e.g. iPod), you can install somewhere else on that, then just run it off that drive.