You failed to include the error message, however, your problem
description is sufficient. In general, you can only use the SMTP server
belonging to the current connection. For more on this issue see
http://www.postcastserver.com/help/Port_25_Blocking.aspx
One workaround is to find out if your home ISP allows SMTP service
on a port other than 25. If not, you can get a free account with Gmail:
http://gmail.com
Then, configure that account for POP access:
http://mail.google.com/support/bin/answer.py?hl=en&answer=13273
Then, add that account to your Windows Live Mail:
http://mail.google.com/support/bin/answer.py?answer=86383
That will give you a separate Gmail account (sending and receiving).
You could ignore its receiving capability and just use the Gmail send
capability while away from home. Gmail's SMTP uses port 465
which is not blocked like port 25 is.
It is also possible to integrate the Gmail SMTP server into your
existing account, but the settings are a bit tricky. Let me know
if you want to go that route.