Hi,
The light at the back only means you have power to the board. If the AC adapter is not putting out enough power or if one of the enclosures other circuit boards is dead it will not power up despite having good power. Of course there's always a slim chance the harddrive inside the enclosure has failed.
This can happen for a miriad of reasons but they really aren't relevant at this point.
If either of the first two is the case your best solution is a new enclosure, if the new enclosure fails to garner results then the latter is the case.
So, head to your local
PC shop and ask the techs there to test you harddrive in a new enclosure, if it works in the new enclosure buy the enclosure and be happily on your way. If it doesn't the hard drive is faulty. If it's just holding a backup of your
data and you have other copies on your computer, buy a new external drive(or send that one in for replacement) and you'll be fine.
If the worst case scenario prevails and you were never taught how to properly protect you data and have a dead drive with crucial files on it then reply back here with your location(Country, State and City) and I will refer you to a nearby facility that can help you retrieve your files.
Hope this helps FixYa,
Chris