Then, most likely, it's the problem in your USB port, or your OS...check if it's clean of any Viruses and try plugging your external HDD to another USB port. Also, which model it is exactly? Does it have have additional power outlet adapter, or is it powered through USB? It is always a good thing to provide us with links to your hardware specs, also - make sure that it's fully powered on, before plugging it into USB port (if it has power outlet adapter, connect it and make sure that it works - put your hand onto external HDD's case and check if there are small vibrations of it starting up, you should feel them pretty easily, and if indication lights (if there are any LEDs on it's casing) are flashing).
My guess would be that your external HDD's model is this one?
It's the "plug & play" type, as long as you connect it to power outlet through adapter and then connect USB cable, you should be absolutely fine.
If it won't get recognized after that, then it's highly possible that it's the problem in your USB port/USB controller on the motherboard, or your OS.
Tried it with other computers and different cables. Still not working.
...well...I'm really sorry to inform you of this, but...if it doesn't work with other computers too, then, almost definitely...it (or it's power adapter/USB connector) died. :\
I think you can still recover data from it, but, I think, it would be best to take your external HDD to the nearest local hardware repair atelier.