EPrompter solves the problem neatly. It automatically checks all of your Web-based e-mail automatically every 15 minutes, and alerts you when any has new mail. You'll be able to do this for up to 16 different accounts. In addition, you don't even have to log into the different Web-based mail systems in order to see your inbox, read your messages, and respond to them--you can do all of that from directly within the program. You can also delete mail as well.
I had problems getting Hotmail to work with this software. One time I tried, if I identified it as Live-mail it worked, but another time it wouldn't work even when I did that. So you may have some setup problems with Hotmail. On the other hand, it's free--and it works fine with other Web-based mail, so it's certainly worth a try.