"socket error #10061" has been in these forums many times, but I could not find a solution that worked. I have been able to receive mail through my POP account, but not send through my SMTP.
I finally found the unexpected solution, and am therefore posting this for the next guy's search.
I use MailWasher to SPAM filter the mail first, and their setup provided the following (spelling/grammar errors are theirs):
"Enter your outgoing server port number, if you are unsure consult your SMTP providers documentation, though most servers use port 25 or port 465 if SSL is supported. Some ISPs block port 25 when you use a server that isn't under their control, try port 587 if you think your ISP is doing this."
I selected port 587 as the Outgoing Server Port Number under Outgoing Server Details and my outgoing mail sends without a problem.