Well, this happened to me, after I uninstalled some program. Internet Explorer 64-bit would open, but IE 32-bit would just not open on my Windows 7 64-bit. Nor would Internet Explorer No Add-ons open. When I clicked on the icons of these two nothing would happen; but when I clicked on the IE 64-bit icon, it would spring to life.
I might not have noticed it, since I have the IE 64-bit icon pinned to my taskbar, but when I tried to click the links on my Twitter clients, the default browser, which is the Internet Explorer 32-bit, would not open. Nor did any links open when I clicked on them in my default mail client, Windows Live Mail. I would get the message: