Usually a USB hard drive is simply a standard hard drive in an enclosure. You could potentially disassemble the USB drive and connect the bare drive up inside your computer and see if it is detected or usable there.
There's a nice guide to what to do in this eventuality here: How to recover the USB hard drive which is not recognized by the PC
There are several guides on youtube that walk you though installing a hard drive in a computer, but just to test the drive you can skip the actual mounting of the hard drive and simply connect it up. I'd recommend putting a piece of cardboard underneath the hard drive to prevent it shorting against anything.
Short of opening up the PC there are also several adapters for hard drives which allow connecting the drive directly to a USB port. These can be useful for several reasons and I always have one handy. However this option involves a small cost (and the time to go get it) unless you can find a friend who happens to have one.