I've passed these things through airport XRay scanners all the time, it usually isn't enough to damage it.
One thing you can do is when you connect it to your PC, click start, then RIGHT click on "Computer" and choose "manage" and then open Disk Management. See if the drive is showing up in there (it'll be easy to see because the drive will show the FAT file system as the format) and see if maybe the system is giving it a drive letter that the system already has assigned (this is pretty common on external drives actually)
Now one question I do have is did you format it as FAT or FAT32? It shouldn't matter for Windows, but it helps us to know what to expect.
I've had cases where this has occurred before - someone saved data to an external drive using a Mac, formatted the drive correctly, but the PC wouldn't read the data. It's likely still there, just not entirely FAT-formatted like the Mac intended. If that's the case, and the drive letter assignment isn't the reason, you might want to get some software like Catacombae - HFSExplorer