kwplee

What OS do you have? What brand and model of your new ext HDD?  
Some brand or model of ext HDD requires extra USB power to run, like Maxtor OneTouch 4 Mini comes with its own double USB power plugs.  WD Passport comes only normal USB cable but works fine.
Also some old system doesn't have extra power cable installed on motherboard, their USB ports won't have enough power to boot the HDD.