Never mind, everyone, I solved my own problem. My Kindle now works just fine with my new USB3 ports.
Here's what I did: I connected my Kindle to one of my USB3 ports. As usual, nothing happened except that "clank" where the computer acknowledged the existence of the Kindle.
I went into Device Manager. Suddenly a new subdirectory appeared: Portable Devices. Clicked on that & saw "Kindle." Clicked on Kindle, and then right-clicked on Kindle and chose "Update driver software."
A minute or so later, the computer told me, "Could not complete update because could not turn Kindle on." Well, duh, it was already on! BUT, my Kindle had magically appeared in Computer and I could do everything except recharge from the new computer.
I turned my Kindle off. Then I repeated the whole "Update device driver" routine. THIS time, the computer turned the Kindle on AND restarted it. And problem solved. My Kindle has returned to working perfectly with my new computer.
Incidentally, if anyone is interested, I have more than 200 screensaver images in my Kindle, each of which identifies the Kindle as mine (in case I lose it somewhere). Here's how I did it: http://witwisdom.wordpress.com/2012/08/06/customize-your-kindle-screensaver/.