Outlook Express downloads mail from the server (in your case, sounds like you use Yahoo) to your computer. It stays on your computer unless you delete it. The web-based mail, such as when you go out to Yahoo to read your mail, stays on Yahoo's server (on the web) until you either download it or delete it yourself.

Sometimes OE doesn't work because the ISP service is down for some reason and you just can't get out to their server to get your mail. Sometimes Internet Explorer also doesn't work for the same reason. Sometimes it's just that there is heavy traffic and the web is busy. If it consistently doesn't work after fixing the firewall issues, you may need some outside help from someone who can come and look at your setup. Someone from tech support from your ISP provider should be able & willing to walk you through fixing the problems.