Potatoes that don't cook

Yesterday I made two crockpots of potato, Italian sausage soup. One for home and one for work. I make this all the time - never an issue. I cut up one bag of potatoes in small pieces for one pot and another bag for the other (1 from Publix Grocery and 1 from Wal-mart). Started the same time in chicken broth and wait till the spuds soften to add anything else. The work pot with publix potatoes was completely done in 5 hours, the Wal-Mart spuds had not softened after 7 hours.
I have read other comments and ideas but I think it simply has something to do with the spuds themselves, maybe storage or grade. All other things being equal - these red potatoes will not cook. Because of the cost to make this soup, I am going to try turning the crock on for a couple of more hours and see if that helps-I actually considered the food processor.
I really think it is the grade or storage - not the first time when buying from WM. Anyone want 3 qts of raw potato soup?

Make sure you are putting the potatoes in cold water before they go over the heat. This will help even cooking.

Umm… The green color is harmless chlorophyll, caused by a reaction to light and warm temperatures. However, it can be an indication increased levels of solanine and related alkaloid compounds may be present.

Solanine is part of the plant's natural protection system and is normally present in small amounts throughout the plant. When the potato is improperly stored or begins to sprout, it reacts by producing the toxin which tends to accumulate near the skin, eyes and in the sprouts. Alkaloids are bitter and that's really the only way of telling if solanine is present.

You will find recommendations from knowledgeable sources that range from cutting away the green parts to discarding greening and sprouting potatoes altogether.

That has happened to me one before, also in a stew (about 20 years ago). It was traumatic to me and I have never gotten over it! I do not know the scientific explanation, but I remember that that particular potato had a slight tinge of green right under the skin. Since that time I have avoided using any potato with the slightest hint of green under the skin, and the problem hasn't recurred. Sorry I can't be more specific, but I hope you are assured that the problem is not you or your cooking method.

The most common problem I've seen with cooking potatoes is when whole potatoes boiled for mashed potatoes. The problem is that they are usually added to piping hot water.

I've found that whole potatoes cook best in liquid when they are put in the pot while the water is cold. This way, the potato slowly heats up with the water and cooks through evenly. When you add potatoes to water that is already boiling hot, the outside cooks really fast and disintegrates while the center tries to catch up.

Obviously there are many other ways to cook a potato and each way will require a different answer to this question. Different varieties of potatoes have different properties and sizes which also will affect the method you use to prepare it and what dishes they work best for.

What kind of potato? What size?
What method of cooking?