Thee is no "outlook express" and hasn't been since Vista. Vista introduced Windows Mail which I believe morphed into Live Mail, which is still part of Windows Essentials 2012 and can be obtained from here http://windows.microsoft.com/en-US/windows/essentials You can pick any one or all of the components you wish to install.
So if we're talking about Live Mail, then you may need to reinstall it to get it up and running properly.
Hotmail is typically a web-based program. You just open a web browser and go to www.hotmail.com and log in with your account name and password.
The new and somewhat generic "Mail App" is a local interface (mail client) in which you can (if you want) add your Hotmail.com account as well as others if you like.
Just a quick note, in case you get confused. Hotmail was retired in 2013. But it was , effectively a change of name. If you log in to Hotmail, the page will open as Live mail. Your account should be intact.
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