WD My Book not powering up

I have a WD MyBook external hard drive that is not powering up. When I plug it in, the light turns on briefly then turns off. My computer does not recognize it. I had purchased a compatible plug to see if that was the issue, but it was not. What other things should I try? If this is no longer functioning, I need to get all my information off of this thing… any suggestions? Thank you!