The first thing that comes to my mind is, does this external hdd have its own powersupply or does it receive its power from the USB ports only?
If it has its own powersupply, check with iOmega: https://iomega-na-en.custhelp.com/app/home
and see if your hdd requires drivers for Windows 7. In years past, iOmega required drivers for all of its stuff whereas other products you could just plug into the usb and they would work.
If it receives its power from the USB ports, try to use a cable that has two ends for the USB ports, it could be just a lack of power. I have 1 TB (not iomega) that would not work from my front USB ports but will work from the rear USB ports of my desktop.
Let me know how this turns out for ya...