(Light off indicates the power adapter is not connected to power.) Try connecting the drive to a different computer. Switch to a new cable if the current one is damaged. Try a different USB port on the computer.
Quick Tips to Fix Problematic Seagate External Disk: Is your Seagate external hard drive not working? This page covers comprehensive solutions to fix Seagate and other brands of external hard drive not working, not detected, or not showing up errors, making your hard drives work again without losing any data.