I also have a Seagate... I think you just need to set a letter for the volume and it will come to life.
I did this.
As above, used computer management.
1 Type "computer management" in the search bar after you click on the start button.
2 Right click and "run as administrator"
3 Look into the left side of the columns.
4 FIRST click on device manager, and go to USB (universal serial bus controllers) and uninstall, install the mass storage driver... (just in case as in the first responses above).
5 replug your hard drive, and whilst still with the computer management
6 Go to Storage/disk management. In the bottom pane window where you see the partitions, (with the coloured bars on top graphically showing you the disks) you will find one of them, your external HDD, with NO letter.
7 Right click over the offending no letter drive (the one you re-plugged in) and choose "change drive letter and paths"
8 Select a letter but choose wisely! NOT C or D or something that is in normal use, something else.
9 Windows will then pop up and register your external HDD just like when you plug in your phone!