If it is a matter of just the power supply failing, you can get a replacement. It is possible to remove the HD and place it in a new case with a new power supply, as well. However, if you suddenly smell something burning after that, you are on the trail to adventure. That might be a burnt out diode, easy enough for a PC repair shop to replace. Or, it might be something more serious and you would need an expensive data recover shop to get back your loss. You could call Western Digital customer service and see what they have to offer in terms of a power supply or make use of the following link:
If it's the power adapter then a simple search of the internet should show you where to go to find one. The other problem is that the HDD may be bad. You'd have to open the case, remove the HDD then connect it to your computer. I'm sure this would void the warrenty. However if it is the HDD then you saved yourselp the cost of a power supply.