Wondering about somethings here...
Assumption is that it worked on the old computer and the external drive is OK... but is that really the case now?
So I ask if you have tried it again on the old computer just to verify the external USB drive works fine?
Next what are the spec's (make and model) of the new computer? What is the hard drive type (make and model, and USB speed if known)?
Just how are you trying to copy? Windows Explorer? Command prompt?
I'm sort of thinking there is an incompatibility between the new computer (maybe USB 3.0) and the External Drive (USB 1.x or 2.0)?
If the old computer is still working, can you transfer some files to a USB Flash Drive and then take it to the new computer and does that copy off the files fast enough?
Another question, can you OPEN a picture on the External Drive into an application (which one are you using?) on the new computer?
Lastly, why did you suggest the CD that came with the camera? What did you think would be on that that would help? Usually it only contains the camera manual, driver, and utility for the camera and a photo application? Shouldn't have anything for an External drive or even USB ports?
Does the new computer have any other USB devices, network, printer, web cam, etc.? Do these work OK?
Just trying to see what works here....