An error occurred while loading the appletPlease contact support to resolve this issue.Fatal error occurred (5): null
Is it all LWJGL apps? or only applets?
have you tried downloading the tribal trouble demo.
have you got the latest openGL drivers installed?
what are your computer specs?
error 5 usually means that the decompression of files has failed, if you grab the latest nightly build of lwjgl and try that http://www.newdawnsoftware.com/hudson/ it should give you a more meaningful error when it fails in the console.also if you could post an example of your applet here others maybe be able to have a better look at your problem and html code.
OK, firstly not all the applications you list use LWJGL (e.g. WurmOnline uses JOGL), you can get the latest opengl drivers from your video card vendor (in your case http://support.amd.com/us/Pages/drivers.aspx ), it part of the normal driver for your card.
The best thing to do is to create a small test case where the issue occurs. That makes it easier for people to provide a patch to solve the problem. You are of course also welcome to provide the patch yourself