Fixing Your Crappy AT&T U-Verse Connection: What Works for Me

So after AT&T shoved U-VERSE down our throats their regular outages became even more annoying.
Before, it would die, we would wait some unspecified period, and it would eventually come back on.
Now, it dies, but when it comes back on we STILL can't access the internet because their Nannyware blocks most browser connectivity.   In my case, I *can* access sites that make use of a Secure Socket Layer, but nothing else.  So I can get on my Amazon seller account, but not browse Amazon itself.

And this will *not* fix itself, in spit of all their diagnostics turning up green.

The AT&T helpdesk being worse than useless (blaming ME because THEIR software can't handle an unexpected modem reboot), the internet not providing a complete answer (clearing out my registry with a program like CCCleaner is helpful, but only *after* I apply my fix), I discovered a cure through pure trial and error.

Which I will now share with the world, in the hopes it helps someone else out.

So when your modem re-sets and you get that idiotic THERE IS A PROBLEM WITH YOUR CONNECTION screen, click 'Device' on the menu bar and enter your Device Access Code (which I have memorized, giving you an indication of how frequently my connection dies).  Then you want to RESET DEVICE.  This should trigger a countdown with a big warning paragraph.
Eventually the browser window will go blank and tell you it 'cannot connect to that page'.
Shut down your computer.

I have my own wireless router, which I re-start after the power down.

Turn your machine back on.
Run the aforementioned CCCleaner.
You should once again be able to reach the entire internet.

In closing, U-Verse sucks and you should avoid it at all costs.
If, like me, you have limited broadband options and can't avoid it, keep this workaround in mind.