Cheapest option and easiest test is to plug it into a diffrent usb slot.
2nd try using a diffrent usb lead.
If the cable is faulty then its fixed with a new cable.
3rd as above you need a usb to sata lead from ebay. You will have to dismantle the external drive to gain access. To connect the lead from ebay. But maybe open the casing first.
If its a physical issue with the drive its going to be costly. So you need to explore as many cheaper options first.
This is an example of what could do the job. http://m.ebay.co.uk/itm/USB-2-0-to-SATA-IDE-2-5-3-5-Hard-Drive-Adapter-Cable-SY-/180644338624
If you have dropped it as its been turned on then it could be physical issues.
This is why the cloud is becoming more popular as a 2nd back up.