It sounds like the USB interface circuitry on the external drive is no good. As Pilk stated above you may have to remove the drive from the case and plug it in directly to your motherboard to recover the data. If you are unsure on how to do this or squeamish about opening up your case then you can get a USB HDD adapter like this: http://www.newegg.com/Product/Product.aspx?Item=N82E16812156034
It will aid you in your data recovery. I use a similar type of interface for data recovery and other work on drives. As long as there is no clicking or grinding noises coming from your external drive it is probably recoverable.