I searched the net again, and someone said that they had the same issue (i..e. the Nook won't connect on FIOS) and that they had fixed it with a software upgrade to the Nook.
According to my Nook, it had software version 1.1.0, and the latest upgrade, as of December 20th, is 1.1.2. The upgrade is supposed to be automatically installed by the Nook via the Wifi.... but since the Wifi is not working... it can't get the upgrade to install the fix to connect to the Mother Ship to get the upgrade.... and so on.
So I followed the instructions on the B&N site to download and install the 1.1.2 upgrade manually, and now the Nook connects.
So, it was a problem in the Nook after all. I am somewhat miffed that the B&N support staff did not know about the problem and the fix. Instead they just told me (over and over) to call my ISP and have them put the MAC address into the router... even though I told them that MAC filtering is OFF. This should have been a 10 minute fix over the phone, not an entire weekend of internet searches. Not very good support in my book.
Anyway, now I can connect, and that is all water under the bridge.
Thanks to everyone on this forum for helping me with this. Now that my Nook ST is working, I really do like it a lot.