I get an illegal operation going to any web site.

This usually means there is something wrong with the browser.  Reinstalling the browser you use would be the first step to try.  However, this is difficult if you cannot open any web sites.  If you still have the original installation software for the internet, run that again and try your connection.  If it still messes up, it may be a problem with Windows, or a piece of software that's conflicting with your internet connection.  These will require a lot of troubleshooting to figure out what is causing the conflict.  Remove any recently installed software, and check your device configuration under the device manager for any conflicts.  It could always be a faulty memory chip or processor causing your problems, and the only way to find out would be through trial and error.  If none of the above options work, the only thing left is Windows, so reinstalling Windows would be the next step.

These things will probably require the help of a computer technician if you are not familiar with them.

Refer to Microsoft article #Q175703, #Q150314, and #Q82710 for more information.