So you are saying that your media drive does not show up on the Desktop? Is the media drive internal or external? If it is external, does it power up?
If you open "Disk Utility" (in the Applications->Utilities folder), can you see your media drive there? If yes and if it still does not mount, you probably should try running
DiskWarrior on the drive; if you were digitizing while the power went down most likely the file structure of the drive is damaged; DiskWarrior most of the time can fix these problems.