Hi there J72,
Yes, it is possible that the ac adapter is faulty. You will have to try connecting the drive with another one. If the issue persists though, there is also a possibility that there is something wrong with the enclosure. If this is the case, you will need to take the drive out of the enclosure in case you need the data. Keep in mind that this will most probably void the warranty. If you don't need the data and the drive is under warranty, I guess you can contact the manufacturer.
Hope this will help,
D_Know_WD