How to resolve repeated emails asking for verification of my Apple ID?
I have seen this problem where internet explorer doesn't open certain web pages. It may be an issue with internet explorer not having SSL enabled. In internet explorer go to the Tools menu and click internet options (you can also get to internet options from control panel). Click on the advanced tab and scroll to security, make sure there are check marks where it says SSL 2.0 and 3.0 and then click apply.

If that doesn't work just install another browser like safari or firefox.