What kind of partition does Disk Management list for your external drive? If the drive is listed as a RAW or UNALLOCATED partition, then it means it's not formatted. If it is listed as Primary, Active, Healthy, System etc... then that should mean everything is still intact as it was before and we need to figure out why Windows doesn't want to mount the drive.
In Disk Management, is it assigned a drive letter the same as another drive by any chance? I've had this happen before. If this is the case and you can't change the drive letter of the external, then just change the drive letter of the other drive that's assigned the same letter. You may need to reboot again though for it to show up in My Computer.
Ok, so Windows isn't mounting the drive for some reason. Right click on the drive in My Computer or Disk Management, doesn't matter which, and click properties. Tell me what it says the file system and type are. It should say NTFS and Local Disk.
Once you check that, go into Device Manager and click on your computer name at the top of the list and click the scan button right above that on the toolbar. See if that detects anything. If not, shutdown the computer, unplug the drive and rescan the computer for hardware again once you boot back into Windows so that it'll detect all hardware without the drive. Then just shutdown again, plug the drive back in and rescan again with the drive connected and see if we can trick Windows into seeing the and autoassigning a drive letter to the drive again. Sometimes you can get Windows to detect it again on it's own.
Maybe I'll think of more to try by the time you respond if none of this works.