From a troubleshooting perspective there's a handful of things to consider. We should start from the ground-up. Let's consider the following:
- Is the device receiving electricity? (If you plug something else in that same socket, does it turn on?) <check this one when your hard disk is NOT working>
---- If the answer is yes you may have a fault in the electrical wiring to the device.
- Does the device have a toggle or similar switch to turn on? If it is fouled you may not be making a good electrical connection. <play with the switch; does it flicker or give you unpredictable results?)
---- If the answer is yes you may have a faulty switch (or button, etc.)
- Does the device make (excessive) noise when it is turned on?
---- If a lot of noise, or a scraping or grinding sound, you have a physical issue with your hard drive. A protectionary measure may be the auto-off feature which you could be seeing.
- Is the device plugged into your computer? (We want a good connection)
---- If no, you should plug it into the proper port-type (such as a USB?)
---- If yes, please ensure you're plugging it into the proper port-type (if not the proper port-type you could be causing an electrical short; check the device's documentation)
In any event, if none of the above helps you may do best by checking the owner's manual or searching for one on the Internet (usually available for free in .PDF form.) You could also take it back to where you bought it and have them take a look at it. In any event there's only so much that can be done vicariously. A tech may ultimately need to get his/her hands inside to resolve.
Good luck :-)
If it's worth doing, it's worth doing right.