External hard drive not working

Couple things to try, disconnect all other USB devices, only use the ext drive.
You can also check to see if the drive is appearing in Device manager when you plug it in, make a note of what it detects as. Try it in a laptop or other PC too.

Thankyou sooo much for this help...although i have tried using it on my tv which the usb plugs into media player...which it is not recognised on either  
It doesn't come up in device manager either and i have tried on multiple laptops (few teenagers in the house). Not sure whether a computer shop would be able to fix it or whether its something that is a common problem...just majorly annoying! Thanks again!

could you remove it from the external case and connect as a second drive in your system to see if it will be detect

Problem with that is that many of these USB drives have only a soldered on USB connection and some proprietary 6 pin connection that the data recovery labs use. You will have to pop the case on it to find out, but if the drive inside has a normal SATA connection then great. We will need the model number to determine that. Sounds to me like this drive is dead though.