|What is the model number of the external enclosure ?|
Are there any markings beside or near the jack on the external enclosure the power adapter is supposed to plug into, or specs on a label ?
E.g. if the enclosure has a 3.5" hard drive inside of it, the power adapter must supply at least 12v - e.g. 12v DC, markings showing the center pin is +, xA (x being amps required).
Do you have the supposedly dead power adapter to examine ?
If yes, are there marking on it ?
If you do have the power adapter, there may be nothing actually wrong with it.
The USB connection to the computer must be able to supply 500ma at 5v from the USB port it plugs into.