Is this one of those external drives built around a laptop (2.5 inch) drive? Some of those are provided with a special cable that allows you to plug in an extra USB port in case one port can't supply enough power. Usually, the "computer" end of the cable has two heads, one for data and power and the other for just power (the data pins are not active or not present). You might check, if this is the case, that you have the correct cable ends connected, or try plugging both plugs on the computer end of the cable in to two different ports and see if the drive comes on line.
Of course, if you see a power/activity light on this drive already, then it's probably as others have said with regard to having the right software for NTFS filesystem usage.
Good Hunting, and I hope your problem gets solved.