Is my phone system trashed?

Troubleshoot first. Check to make sure the phone line between base and phone jack is secure on both ends. Try another phone cord, jack, or even another phone if available. That way you can narrow down where the problem is.

If that doesn't work, then through internet or calling from another line contact AT&T so they can troubleshoot from their end to see if it might be the line itself and not the phone.

Traditional landline? If so check from the NID with a known working corded phone. If still bad report to the phone company. If digital service try resetting the move.

Spoom, that worked. It's VoIP; I unplugged the power cord at the base unit, waited a minute, then plugged it back in. Sure enough, my dial tone returned. Thanks.

Now, have you any idea why the system decided to just go belly up like that for no  reason that I can tell?

First did you power down your phone systems base unit or did you power down the modem?  I'm betting the modem and what that does is cause everything to sync back up. 

No, spoom, all I did was unplug the phone base unit, let it sit for about a minute, and plug it back in. I never touched the modem.

Thanks for letting us know.  I would have thought resetting the modem would have been the solution.