I checked my settings, and sure enough, Cookies for twitter.com were being blocked. I changed the settings and...bingo! I'm in!
Now, I will definitely take blame for not thinking of Cookies first -- though I suspect a whole lot of people don't think of Cookies first. But I should have. But...how hard would it be for Twitter to put on a page that someone has clicked to get help about not being able to log in that say -- "Check to make sure your freaking Cookies aren't being blocked"??!!!!
Though I suspect they would use "freaking."
But the important thing. Mission Accomplished!
The unimportant thing: I can now tweet again.
But the cool thing is that I am all the way up to 7 people following me! I like to consider them my minions. We can have club meetings and everything.
For anyone else who wishes to join in, the