cannot send messages from my btconnect account

The SMTP settings in Mail for that account are incorrect if you cannot send but can receive mail on that account

see this

http://www.apple.com/support/iphone/mail/

and the settings are likely these for BT

Host name >>>>mail.btinternet.com

password >>>says optional but use your password

Use SSL >>>on

Authentication>>>password

Server port >>>465

Then try remove them and reinsert from account settings

or better delete account and recreate

when you have the detail correct you get a verification tick against each line

You're welcome