Call from computer telemarketer - spiel said "We're looking for an advertising home in your neighborhood...", disconnected the call at that point & blocked the number.

It is a telemarketing call. If you call the number back, they have an option to take your number off their list.  However, my number is private and on the "national do not call list".  How does this happen?

"However, my number is private and on the National Do Not Call list. How does this happen?"
Simple. Most likely the call you received was auto-dialed, meaning by a computer. It was programmed to call an area code + prefix + 0001 thru 9999 in a specific area in a particular state and the individual who programmed it could be located anywhere in the U.S. or in a foreign country. The automated dialer doesn't know if a phone number is private or unlisted. All it knows is to dial the numbers that where programmed into it and it can dial all the numbers at once. The brief silence you hear when you answer the phone is the call being connected/transfered to the next available person in a call center that could be located anywhere.
My rule of thumb is this -
If someone calls me, regardless of who it is and starts asking me for my personal info., I will refuse to give them any and hang up. Why? Because you can't verify the identity of the person who called you and you can't verify the name of their so called company either.

Not recognized, didn't answer, no message, checked 800notes.com, misery loves company, blocked.

Answered phone.  No response but sounded like a picture was taken and then they hung up. Scary!!