First, make sure that ALL of your graphics drivers are up-to-date, all Windows Updates are installed, et cetera. Restart and then do the following:
1. Use CCleaner to uninstall ALL versions of Java
2. Delete all jagexcache folders, and EoC beta files
3. Run a disk cleanup with CCleaner, make sure to check Sun Java
4. Go into Google Chrome. Go to Settings -> History -> Clear all browsing data -> Only check 'Empty the cache,' & 'Delete cookies and other site and plug-in data,' and click 'Clear browsing data'
5. Close Google Chrome, and rerun disk cleanup with CCleaner
6. Open up Chrome, and go here:
http://www.oracle.com/technetwork/java/javase/downloads/jre6u37-downloads-1859589.html
7. Download and install the Windows x86 Kernel version
8. Repeat step 4 & 5 and then restart your computer
9. Travel to Runescape via the homepage @ Runescape.com, and navigate to the game through the normal website.
10. Accept any Java permissions pop-ups, and choose 'Always run' or 'Always allow' if asked near the top of the page.