KERNEL32.DLL is not part of IE, it's part of Windows 98. You can try reading through http://www.google.com/search?q=kernel32+%22Internet+Explorer%22+%22illegal+operation%22+site:support.microsoft.com , but I doubt if it will be very helpful.
You don't tell what programs you downloaded, so I don't know what you did already, but I suspect some form of malware, or a badly chosen popup- or adblocker. I should start with running spybot, adaware and cwshredder. In cwshredders report you should take special notice of browser helper programs installed. Anything but adobe and media player is suspect, I think.
Hope this helps.
I have had a problem with my IE6.0,,,,,I can not open it.I get an illegal operation in KERNEL32.DLL at 018f:bff876d2 every time.This has been a problem for a few months,so I must use Firefox.I have not found any help from programs that I have downloaded.When I go to start,run,msinfo and select internet explorer,File Versions, KERNEL32.DLL is not there.