Hi Helen. The correct sentence is: Neither my parents NOR my sister likes sports. From GrammarBook.com : Rule 3. The verb in an or, either/or, or neither/nor sentence agrees with the noun or pronoun closest to it. Examples: Neither the plates nor the serving bowl goes on that shelf. Neither the serving bowl nor the plates go on that shelf. http://www.grammarbook.com/grammar/subjectVerbAgree.asp

The answer you received a few days ago was correct. Mikkel's answer is correct.

first : It is ( nor my sister) not ( not my sister ) . 2nd : I do not remember if it was like or likes , sorry.