You can still "give" your account away. Sort of. I believe you need to email blizzard and have them wipe it. And then you must delete all installs and transfer all hardware, etc.

B. You may permanently transfer all of your rights and obligations under the License Agreement to another by physically transferring the original media (e.g., the CD-ROM or DVD you purchased), all original packaging, and all Manuals or other documentation distributed with the Game; provided, however, that you permanently delete all copies and installations of the Game in your possession or control, and that the recipient agrees to the terms of this License Agreement. The transferor (i.e., you), and not Blizzard, agrees to be solely responsible for any taxes, fees, charges, duties, withholdings, assessments, and the like, together with any interest, penalties, and additions imposed in connection with such transfer.