I hate be the bearer of bad news..but soft crown shaft sounds very bad. On almost any plant..a shrinking trunk is fatal. King palms don't take being dug up well. But if yours is simply a big nursery bought plant..take it back-with receipt.

here is a pic of the palm in question. Is there anything that would cause this or that might aid in possible recovery?

The one on the left looks very stretched out. Was it kept in a low light area? If so,its going to take time to acclimate. One very good sign is that the crownshaft is green..not discolored.
If that "bandage" is covering anything gooey...treat with hydrogen peroxide. There are more expensive remedys..I just have never used them. The palm board at palmtalk.com people would know about using antibiotics and the like.

Actually the white is not a bandage it is where the last piece of the trunk that falls of didn't completly fall off.

The section that is spongy is only about 3 inches long and feels almost moist inside.

Should i hold off on watering. It was transplanted about 3 weeks ago. Im in Southern california and temps are in the 60s and 70s right now.

Here is a larger pic of the palm

They normally shed old leaf bases. Nothing to worry about. The soft and spongy sounds bad..but the Palm look normal, if a little on the thin side. It should outgrow the gawky look.

I am hoping so. Should i water it or let it dry ou a bit. I really watered it well when I transplanted it.

They love water. Unless we get a very rainy winter.and some mulch too would help. ALL things transplanted like mulch to keep the soil moisture constant and even. Cacti are exceptions of course!

Thanks for the help I will keep you posted