I don't know why Thunderbird is able to send, but the normal reason for not
being able to send when away from home is a port 25 block.
As a general rule, the owner of the port 25 SMTP server must be the same
as the one providing your Internet connection at that moment. For more on this
see
http://www.postcastserver.com/help/Port_25_Blocking.aspx
The available workarounds when sending away from home are as follows:
1. Use webmail for sending (via your browser).
2. Ask your home ISP if they have a port other than '25' for SMTP.
3. If you use the same away-from-home connection frequently, substitute the SMTP
server belonging to that connection. This is a bit tricky, but if you want to go that route,
I can provide more details.
4. If you frequently send from multiple locations, get a free Gmail account,
configure it for POP access, and use that for your sending chores.
Gmail uses port 465 for SMTP, which is not blocked like port 25 is.