You said you recently installed Win 7, what raises a red flag is the final part that you mentioned. "I see two or three random web sites flash on the monitor before it shuts down." Could you identify any of these pages for me? It can help narrow down the search a lot.
Its possible you've already infected the computer, fresh installs don't have a real defense so while it may seem strange or unlikely I would rule out infection by running a few scans there are plenty of free ones out there that should be adequate.
Also make sure you are not being redirected through a proxy setting. You can find this by clicking the gear in the upper right then navigating to Internet Options > Connection > Lan Settings.
This should be set to automatically detect without any other boxes checked. Alternatively you can go through the control panel > Internet Options > Connection > Lan Settings.
Have you tried alternate browsers at all? Do they have this same issue or do they perform as expected? I can't imagine a system today with super low RAM as cheap as RAM has become but how much of your resources are currently being used when you experience this issue. (ctrl+shift+esc watch number of process's and Physical Memory %)
Also are you trying to use IE11 64bit? (yes it exists/existed? try 32bit if you are see if problem continues.)
Try private browsing with IE 11 as well see if the problem continues.