Is this hard drive a 3.5" drive? how can you tell?

It looks like a 3.5" but it's hard to tell based on JUST the dimensions. But since the depth dimension is big enough to support a 3.5" (and the external isn't called an ultra-portable), what you need to look for is a 3.5" IDE hard drive enclosure. Taking OUT the current hard drive will be harder than you might think. Most pre-made external hard drives weren't meant to be taken apart. If it really is the enclosure that isn't working (not the hard drive that's faulty), you should just get a philips screw driver, unscrew EVERYTHING, and try to pry it apart (usually, there are plastic clips inside holding the two sides together. Once you get it open, there should be four screws (two on each side) holding the hard drive inside the enclosure. Simply take those out and unplug the drive. Do the reverse to install the drive into the new enclosure.