I bought a surge protector and the light on it doesn’t work, does this mean the surge protection is damaged?

I wanted to plug in an external hard drive but I’m afraid it won’t be protected from a surge.

The light is just an L.E.D that glows when power is applied. It wouldnt affect the surge protector, but if I was going to spend my money for it I would take it back for an exchange. You wouldn’t want to risk your hard drive on it if you were only pretty sure it worked ,would you?