Removing the HD is a great way to ensure nobody wants the computer and it ends up in the trash. Nobody wants to buy a hard drive for an old giveaway if they can't even afford to get a $350 new computer. Chances are they don't have a HD just "laying around" or the technical knowledge (or CD) to install a new OS.

Writing 0's to the drive will remove all the data beyond what any piece of software can ever recover. Destroying the drive is pointless.