Seeing as the executable name for Internet Explorer is "iexplore.exe" (with just one 'r'), you definitely have malware.
Norton, though it is keeping the malware at bay, isn't good enough to actually remove the source of the problem.
Right now your best bet is to use another (clean) computer to download a portable virus scanner:
http://www.techmixer.com/free-portable-antivirus-download/
You should run it in Safe Mode, which keeps most malware from reinstalling themselves.
MalwareBytes and Spybot are good to keep on hand:
http://www.malwarebytes.org/
http://www.safer-networking.org/
Norton isn't nearly as bad as the others say, but it isn't worth paying for either. Just download the Norton Removal Tool when you're ready to switch. Kaspersky and ESET make superior products, while AVG, Avast, and Avira have decent free offerings.