I have seen a lot of people facing similar problem. Topcoder arena just do not launch and shows some java Exception. Here is the list of solution that might help you.
Before trying this, I would recommend you to check if you have latest version of java installed.
Does not matter if you are using windows, Linux or Mac, goto Terminal/CMD and run command
(without quotes). When you run this command you will be taken to java applet cache windows. Delete whatever application you see there and restart your arena.
In most of the cases you should be able to launch your arena.
If you are not able to launch your arena even now, try solution 2
Sometimes, topcoder arena applet takes a lot of time to run that might cross javaws timeout value. Fortunately, javaws provides us with command line option to change the timeout value.
Run this command to launch topcoder arena with increased timeout:
javaws -J-Dcom.topcoder.net.httptunnel.client.connect.timeout=X http://www.topcoder.com/contest/arena/ContestAppletProd.jnlp
Hope it helps. :)