What OS are you running?
Just because other USB storage devices work, it doesn't mean the camera is automatically at fault. Each OS should recognize the device for what it is, not just as a storage device (even though that is what it is).
For example, Windows 7 has issues with my Canon Hf10. It is 100% OS camera driver related; nothing is wrong with the camcorder.
(assuming you run windows) Also, go to control panel, admin tools, computer management , disk management and see if the device shows up there. If it does, you have a drive letter assignment problem.
Try the camera in another PC and see if it just appears.
Like others said, make sure your cable functions. maybe try it with another camera.
If you test all other options, then assume the camera is at fault. Maybe take it to a camera shop and just have them try to hook it up before sending it in.