Outlook expressoutbox does not get empty

Could be that you are accidentally working offline. Check the menus and settings to make sure this option isn't checked.

Other possibilities are that the account is somehow set up wrong. The mail server that you are connected to might be input wrong.
And similar to this, the mail server itself may be down. Try going to that mail website and sending a mail to yourself directly via the website. If it arrives in your Inbox, then at least you've narrowed it down and know it's your Outlook Express that has the problem and not the connection.

Either the mail is not going out or the sent messages are not being removed from the Outbox. Send a message to an acount you can check if it dose not arrive check your account setup in OE