Someone from this number has been calling me multiple times a day every day for the past week.  One call came in at 12:45AM!  I've had this number blocked for the past year after the last barrage of calls from them.  What is odd is that I have never participated in a survey.  I have an unpublished number, and I'm on both the federal and state Do Not Call lists.  How they got my number and why they keep calling when their number is blocked is beyond me.

"How they got my number ..."
There is nothing special about your number; any other telephone can call it on purpose, or accidentally.
What would be special would be the association of some of your personal information with your phone number.
Many scammers won't have that information; they are calling to try to find out who will answer.

"...why they keep calling when their number is blocked is beyond me."
They are using an autodialer. They don't care that a called number is "blocked" - they might not be monitoring such results at all, or might be hoping the called number will be answered by a gullible human. Some scammers are very small operations, and don't bother to update their systems' databases for a long time, if ever. Eventually this batch of scammers will abandon calling your number as they try another set of numbers to call. But there are many scammers out there, and their calling attempts overlap. So you will get more calls in the future.

I never answer phone calls if I don't know the number, so when this number came up, I looked it up here. And they've left voice messages requesting me to be a participant in their radio survey or some sort. They've called several times and never answered them or called them back.

I had this name "NEILSON" call about 4 times and just called today May 19 and finally left a message
and number to call and stressed that they have been trying to get in touch with me?  I didn't give my
priviate unlisted number out and don't know how they got my number.  I too, answer calls I don't recognize
and don't leave a message?  I want for this company to stop calling me and to be put on the "Do Not Call List",
if there is one.

I too worked in radio and tv and am very familiar with Nielsen and the methods they use to do the "sweeps".  It's legit