How can you tell if your hair is dead?

Your hair was never alive to begin with. It's not a living part of your body. It's part of your excretory system which is why it "grows". It's the same as sweating.

However, if you meant "how do you tell if your hair is damaged" (I honestly wasn't sure), if your hair is breaking off, frizzy, or feels like cotton-candy when it's wet it's severely damaged.