Thank you everyone who advised me on this issue. I did try your suggestions; however, after having no success with them, I bit the bullet and rang up customer service...which turned out not to be very painful at all!

I think I was on the phone for a total of 30 minutes (about 20 of that was on hold, natch), but I was connected with a tech support guy, and he had me dial some ##7744 number (or something like that), and a passcode or two, and basically reset the way my phone connects to the internet.
Upshot is--now I can not only get onto the web and receive my email, I can also SEND email, using my Centurytel outgoing mail server! Woohoo! I am a happy camper indeed.
