You said all accounts but one were green and wondered how one failed account in Connection Doctor could block the rest. If that one account is designated as the sole SMTP server of choice (the only way mail can get sent), then nothing using that "avenue" will work.
Change the the sending email address to one of your other email addresses, and trying sending again. That can narrow down the problem account.
As for testing by sending a self email. . .
I've always been told that sending an email to oneself at the same address (or even the same domain) may not be an adequate test. You should send it to a different domain. In other words, if you're testing the sending functionality of a gmail.com email account, send it to an address with a different domain, such as a me.com or hotmail.com.
Personally when I'm having these kind of problems, I simply delete the account in question in Apple Mail preferences or in the system preferences. Then restart the Mac and add that account back using the Add Account wizard in Apple Mail or system preferences. SAVE A COPY of the stuck email before deleting the account or at least copy / paste them to a text edit document.
Another tip: Test your account credentials by going directly to that email's website. For example, Gmail go to Gmail.com, and use your account credentials to login, thus confirming your username and password are correct. If they won't login there, they're certainly not going to login in Apple Mail.
Good luck.