... after the program supposedly runs I get the message that I have no internet connection.
Which version of Windows Live Mail, on which version of Windows?
To find your program version, in Windows Live Mail press Alt-H A. If that does not show you the build number, press Escape twice and then Alt-F B.
To find your operating system, press Windows key + R, type winver into the box and press Enter.
I have an error connecting with the Windows Live Mail Calendar.
Please see this article: Error when attempting to connect to the Windows Live Calendar service