It took me a while, but I figured out the problem, although not the reason for my problems. The issue of getting mail downloaded went away, and, the, I started getting Page Load Errors. I, simply, could not connect to the Internet, except for my ISP mail. After trying to use new profiles, or trying to start in Safe Mode, I got suspicious of my Firewall, and, sure enough access In and Out were blocked, for Seamonkey only. I made the necessary changes in the Firewall settings, and here I am. And, what do you know, I checked for updates, and there was no change in my Update settings.
Now, why was only Seamonkey affected? May be because it was default. But, it, surely, was freaky, and I, almost gave up on a perfectly good program.
UserAgent: Mozilla/5.0 (Windows NT 5.1; rv:9.0.1) Gecko/20111221 Firefox/9.0.1 SeaMonkey/2.6.1