Hello Richard,
Some things to try first:
Does it have power? Is the power lead working - check the lights on the drive come on. If not then you have a faulty power lead / the transformer inside the drive unit is broken.
It seems like you have tried a stand alone PC and a laptop but was it using the same USB cable? If so then find another one just to eliminate that the cable isn't at fault. Also try different USB ports in both the laptop and PC.
If you get no joy with that then download and install the Data Lifeguard Diagnostic for Windows from Western Digital's website:
http://support.wdc.com/product/download.asp?groupid=304&sid=3&lang=en
Try the quick test and see if the diagnostics can display the drive information including the SMART status. If it can communicate with the drive and displays this information then it is likely the hard drive within the unit that has problems in which case try running the extended test. This will report back any bad sectors within the drive.
However, if the diagnostics cannot communicate with the drive then this would most likely indicate that the drive is either not powering up properly or there is a fault with the controller part of drive. In which case try switching it on and listen to it. Can you hear it powering up? It will also vibrate slightly. If you can't hear that then the drive isn't powering up properly in which case it will need to be removed from the unit and placed into another working unit. You can buy spare hard disk enclosure units which will come with power supplies. It will mean that you will have to open it though - if you're not sure how to do this then most computer shops will be able to help:
http://www.amazon.co.uk/s/ref=nb_sb_noss_1?url=search-alias%3Daps&field-keywords=external+hard+drive+enclosure+case&rh=i%3Aaps%2Ck%3Aexternal+hard+drive+enclosure+case
If you can hear the drive starting up / vibrates on power up then this would indicate that the power supply to the unit is fine but the controller part isn't functioning correctly. Again, the only way to fix this is to remove the drive from the unit enclosure and transplant it into another enclosure case.
If all this fails then you will have to send the drive away for recovery. There is more information on Western Digital's website here:
http://support.wdc.com/recovery/index.asp
I wish you the best of luck,
Alan