Remove the lower case in your Apple TV 1st Generation.
Starting at one side of the device, use a hairdryer or a heat gun to soften the adhesive holding the rubber base in place.
While the adhesive is still warm, peel the bottom of the rubber base upwards to detach it from the metal plate.
Repeat the procedure described above until the rubber base has been completely removed.
Remove the four T10 Torx screws that secure the lower case to the upper case.
Carefully lift the lower case from the upper case enough to allow access to the internals of the Apple TV.
Carefully pull the hard drive data cable straight up from its socket on the logic board.