Presumably mail.btinternet.com is the address that BT gave you as the SMTP server? You might want to try sending via mail.btclick.com or mail.btconnect.com or smtp.btconnect.com or smtp.btinternet.com, BT run quite alot of SMTP servers and you may have better luck with another server.
The fact that it reports that you cannot even connect to it suggests a communication issue. Do you have a firewall between you and the Internet? If so, is it configured to allow a outbound connection to this server on Port 25?
You might also want to rule out the software as the issue rather than the connection by TELNETing to the server. TO do this, just go to Start / Run and type TELNET mail.btinternet.com 25 and hit OK. You should get a response on screen that says "220 smtp814.mail.ukl.yahoo.com ESMTP". If you get this, then you have contacted the server and the issue is with Outlook rather than the connection / other factors. If you do not get this, then Outlook is not the issue.
Hope this helps to narrow down the issue.
J.