Just realized I didn't follow up with this. The end result is that we have the refrigerator (undamaged) and LG did make me happy with their response to everything. That went a long way.
The refrigerator was delivered and was not damaged. It was fine. I think it was delivered by a different third party company than the first two times. For the first two delivery the guy in charge was different on each delivery but the second person was the same one. On the third delivery it was different people and just seemed different.
Interestingly, the delivery guy said that sometimes delivery people will cut the electrical cord on an appliance so as to not have to do a long delivery. On the first delivery, they were running late when they arrived (end of the day). That said -- I didn't have any hint the cutting of the electrical cord had anything to do with the delivery people. The delivery guy said the cord was not in the box.
Anyway -- the delivery went fine and set up went well. This refrigerator is one of the unit with instaview door in door. After the delivery guy left I was going through the refrigerator and taking off all the plastic covering the shelves, etc. In the inside part of the door unit there was plastic that wrapped under the inside unit.
No problem -- the inside door unit is easily removable by moving it up and out. When we tried to do it, though, the unit wouldn't budge on the right side. It would move (or try to move on the left) but the right didn't move at all.
I thought maybe we weren't reading the instructions correctly so we got in the car and went to Home Depot and found a similar refrigerator and asked how to remove the inner door shelving unit. It was super easy. Just up and out. We had been doing the right thing. Went back home and it still wouldn't budge.
I then called the person at LG who had helped me earlier. She had said to call her specifically when I got the delivery and she would arrange an inconvenience allowance. I called and also explained the problem. I told her I was reluctant to try to force the unit as I was worried the plastic would break. She told me not to force it and, with me on the phone, arranged to have an LG repairman (actual person working for LG not a third party) come by to check on it.
We then talked about the allowance. She was limited in how much she could offer as was her supervisor. Therefore, she asked if I wanted her to call the corporate office. I did. She called and they approved payment to me of $300 which will be arriving in the mail. Since I had to spend almost $250 for the small refrigerator this seemed fair to me.
She said that the reason that they approved a payment that high was because I was left without a refrigerator. She said that the policy is to not leave someone with no refrigerator. Even though the electrical cord was cut on the first unit. they were still supposed to offer me a loaner.
Oh -- about the inside the door shelving unit. The day before the guy came by a replacement unit arrived. So I was happy with that situation as well. So far, I am very happy with the refrigerator.
I am still frustrated by the fact it took 3 attempts to get an undamaged unit to me. But, I was impressed with both people that I dealt with at LG. And I feel the compensation for my inconvenience was fair and I wasn't out any money by having to buy a small refrigerator/freezer while waiting.