The send/receive progress box shows the current (only) task as send 2 message(s) using '[my default mail account]' and a status of 0 of 1 tasks have completed successfully

The Stop button is greyed out, so I can't even tell it to give up -- and it never times out even if I wait much longer than the maximum time configured for any connection.

There are dozens of threads here about Windows Live Mail with messages stuck in the outbox -- but none of the 'solutions' are even anything that can be attempted in this case because there is no way to get to any of the controls for Windows Live Mail - what you see in the picture above is ALL there is.