You could run Checkdisk, as maybe something about Windows messed up when you had to hard reboot - it may not be the drive, which would explain why it works ok on the laptop.
Sometimes other weird things can happen. The external drive might need to warm up first. I have one like this - if the drive is cold and I turn it on, everything on my desktop slows to a crawl - music, mouse movements, everything...but let it run for a while and the desktop will snap back, although the drive won't be recognized. So at that point I turn the drive off and turn it on again, it mounts fine and is perfectly usable. Alternately, to avoid the whole slowdown problem, I just take the USB cable out from the drive itself rather than the USB port on my computer, turn the drive on, and once it's warmed up enough I turn it off, plug the cable back in, and turn it back on.