[Plugin: WP-Mail-SMTP] WP-Mail-SMTP with Contact Forms 7

I installed Contact Forms 7 on our WordPress site on GoDaddy. It worked fine out of the box.

I then installed WP-Mail-SMTP (I need SMTP for another plug-in). After trying nearly every combination of settings I could (including those given to me by GoDaddy’s technical support), I was unable to get it to work. I tried both “relay-hosting.secureserver.net” and “smtpout.secureserver.net” both authenticated and not with every possible combination of settings, and I always get one of the following errors:

SMTP -> ERROR: Failed to connect to server: Connection timed out (110)

or

SMTP -> FROM SERVER:
SMTP -> NOTICE:
EOF caught while checking if connectedSMTP -> ERROR: AUTH not accepted from server:

Of course, Contact Forms 7 now no longer works. I get a red error message “Failed to send your message. Please try later or contact administrator by e-mail” within 5 or 10 seconds of pressing “send.”

I then selected “Use the PHP mail() function to send emails” in the WP-Mail-SMTP options assuming it would go back to the way it was, but Contact Forms 7 still won’t work. If I try to send a test message from WP-Mail-SMTP (even to an address with the same domain) my browser spins for about 30 seconds and then I get a blank page. Contact Forms 7 similarly takes about 30 seconds and then returns a yellow validation error message (even though everything was entered correctly).

Any help would be greatly appreciated.