Just tried it again finally--sorry, I've been busy lately. I can't give a yay or nay since now PHPList says "failed" when I try to send a message, test message or not. Once again, I'm not sure if this is an issue with PHPList or with the server. I do know one way of sending messages with PHPList is with PHPmailer, but since Softaculous installed it, I'm not sure if that is even coming into effect.
Just in case, djbob, did you edit phpmail() or how I use it at all? If so, that may have broken something else for me. If not, let me know and I'll pursue it further on the PHPList forums. Thanks for the help so far!