After not having any luck finding the base reset code for MY AT&T 5830 (no answering machine - no display) I stumbled upon a page taking about a vtec system. It had a code. It sorta seemed familiar, like what the support for this phone told me a 5 or 6 years ago.

Punch in the reset code (including the stars): **335782

I tried it. It worked. I was floored. I registered my old working handsets AND the "new" one. Life is good.