Received call from (339) 502-6440 a couple minutes ago on my cell phone

Ok... after about 15 more calls. They will not leave a message and it's very difficult to get rerouted back through a system and make progress without giving them *even more* personal info than they likely already have.

Here's the solution: Answer the call. May want to let it ring a couple times so that the auto-dialer doesn't just hang up on you.

Matter-of-factly tell them that you no longer own the vehicle, let them know that you have been called many times and ask them to be removed from the list.

If they ask for vehicle information so that they can "update your file" etc. tell them that you no longer have a car, that you don't drive anymore, etc. If you like, make up some story about why now merely the mention of your owning a car or driving is traumatic... but whatever you do - Don't give them any additional info. My vehicle record with them was about 5 years out of date... our info seems to have been sold to them by a shady dealership where we had (theoretically -  LONG story) repairs done.

Seems to have worked. We'll see...

keeps calling and will not leave message, or hangs up

Listened and declined their pitch about 2 weeks ago.  I thought that would be the end of their phone calls.  For the last 2-3 days they call my cell phone 5 to 10 times a day.  When I answer their is only dead air.  Today, I called the number back receiving a message simply saying to press "1" to be removed within 24 hrs from their call list.  I had to go online to find out who was calling me.  We'll see if they still call, but their calls are eating into my Verizon cell phone time allowance.

Hello fellow Verizon user !
Log on to your account via the verizon personal account website:
http://www.verizonwireless.com/b2c/index.html ( if you have not setup access to your account via the web, you can from there )
Next go to the Spam controls and add the phone number to the Block list ( you can block up to 10 numbers for free for 3 months at a time, just re-add them when they expire or you can pay about $5 a month extra for unlimited )
Now they can not call you.
If you have a smart phone, like a Blackberry, there are a few apps that can auto-hang up on blacklisted numbers.