The easiest thing to fix is if your power supply is dead. Can you test it with a volt meter?
The usual first step with an external drive, if you are comfortable with hardware work, is to remove the drive from the external case and attach it to the motherboard of a full-size machine. This is to determine if the problem is in the external enclosure (drive will work attached to motherboard), or the more difficult case where the problem is in the drive. Are you comfortable with this level of working with hardware?