That's my problem too although I don't think I have the same problem that TC has (although I use the pop-up blocker with the Google toolbar (free) and it knocks out practically every pop-up.
My homepage goes to one of two search engines - one os called "Lucky Search" and I forget the other one (with a green background). You can go under "Tools" then "Internet Options" to re-enter the homepage you desire.
I've notice that sometimes it keeps on my homepage, even after shut down, and sometimes it doesn't. I don't know what the "triggering" mechanism is but I'm going to start paying attention to when I visit Drudge and see if there's a pattern.
If you find a fix, let me know. If I find one, I'll let you know.