The writers said they intended him to be your father, but they weren't sure if Nintendo was OK with it in the beginning, so they initially left it ambiguously just to be safe. The Japanese site says that you're actually the son of DK II (who was once DK Jr.) and that Cranky is your grandfather, but then again, Japan also says that there's more than one K.Rool, which was obviously not Rare's intention.
-9-Volt regarding the reasons why DK's identity is the way it is as well as discrepancies between US and JP continuity.