How do you tell if a potato is stale/old?

I bought a bag of potatoes 2 weeks ago, and they won't cook. My mashed potatoes turn out lumpy, baked potatoes take 30 minutes in the microwave, instead of 6 minutes like normal, and I gave up on the baked potato in the oven after almost 2 hours. I've never had this happen before. They look fine, they small fine, but they won't cook! I read somewhere online that they might be old or stale. Is there any way to tell? Is there anything I can do, or should I just pitch them?