Thanks again, @ADFENO.
I upgraded to 38.5.0-1~deb7u1+7.0trisquel2 and still have the same error:
"Sending of the message failed.
The message could not be sent using Outgoing server (SMTP) [*****.com] for an
unknown reason. Please verify that your Outgoing server (SMTP) settings are
correct and try again."
I also tried using Thunderbird and sending from the account I was having
problems with worked without problems.
Why isn't this problem happening to more people? Why am I able to send from
some accounts but not others? Why does it work on Thunderbird but not
Icedove?