I have now updated the client, and made some changes which should fix this problem, so if you were having trouble please try again.
The problem only occurs if you have an extremely old version of Java so most people weren't affected anyway.
However if RuneScape STILL wont work for you then visit www.windowsupdate.com and get all of the 'critical' updates listed there. This should fix the problem. This also has the added benefit that it will fix any security problems your computer has. So if you don't want to be hacked you should visit windowsupdate.com on a regular basis anyway!