My Book Live won't turn on-Please help!

Welcome to the Community.

It’s possible for the Power Adapter to be at fault. If so, WD Support can provide you with another one under warranty. You can do so either by phone or email.

To Contact WD for Technical Support
http://support.wdc.com/contact/index.asp?lang=en

Support by Country
http://support.wdc.com/country/index.asp