necessarily with your computer.

There is a distinct possibility that your HD is no longer with us. Shuffled off this mortal coil, so to speak.

Yes, it happens and sometimes with no warning whatsoever. The good new is; The Seagate drives have quite a long warranty and yours may still be covered.

If it is any consolation, and I'm sure it's not, my internal 500Gb did exactly the same thing to me on Tuesday.! Just up and died. I even got the same error message as you.

Check the warranty.
If it's not under warranty, you can still use the enclosure to put in another, larger HD.