Windows isn't designed to be a secure system like that. So anything you do, can easily be circumvented. Mostly because Microsoft decided to bolt IE onto the rest of the operating system. So, now, any window used to show files, can also be used as a web browser. To limit access to IE is to basically limit access to the entire system.
The longer answer is that there are some things you can set, but then you have to change them EVERY time you want to allow access to the Internet.
You could do this real easily with a Linux box... MAYBE even a Mac, though that gets a bit more iffy. Windows makes it a giant pain in the **** to do effectively.
How can we prompt for a password when accessing the internet using Internet Explorer or any other browser?