Q: BTinternet email will not send from imac but will from iPad.

I have three mail accounts set up on my imac. One BTinternet, and the other two hotmail accounts. In the last few days for no obvious reason I cannot send from my BT internet account.  After trying to send for a few minutes I keep getting error message that connections to host smtp.mail.yahoo.com on the default ports failed.  BT internet is not blocking the SMTP ports.  The SMTP outgoing server is listed as BTinternet(offline)! This seems to be a reasonably common problem, but nothing I have tried works.  Any suggestions gratefully received, though I have minimum technical knowledge!