[2015-02-23 : DLL-Files.com support says:]
We believe this file is a part of a malware blocked by your security software.
It seems to belong to a toolbar of some sort.
Try starting Internet Explorer without extensions, and remove any new/suspicious extensions. Then try starting normally again. In Windows 7, to run your Internet Explorer in the no add-ons mode, Open Start > All Programs > Accessories > System Tools > Internet Explorer (No Add-ons).
Quick method: press Start key+R to bring up the RUN prompt. Run the following command: iexplore.exe -extoff
A search indicates that t8ExtEx.dll belongs to the FunWeb/MyWebSearch family of potentially unwanted programs.
Go to Control Panel> Add or remove programs and uninstall any of these that are listed: Mywebsearch Bar - Smiley Central - My Way Speedbar - Search Assistant Mywebsearch - Fun Web Products - Fun Web Products Easy Installer - Weatherbug Companion - maps galaxy toolbar - mind spark -