I lived in Hawaii from december-september. I registered to vote and worked but never got a state ID, what do I put as the date I became a resident?

Your "domicile" (residency) is determined by a number of factors - where you register to vote and where you have a driver's license or state ID are just two of them.

In a sense, what is more important is your intent. When did you intend to set up Hawaii as your domicile? Did you establish a mailing address in Hawaii and tell other people about this (I assume you at least did with the voter registrar)? When did you move into the place where you are currently living? 

Generally, when you change where you live and tell people that you live there, with no clear intent to return to where you came from, you have changed your domicile. So what day did you "move in" (understanding that this could be a short term rental as well as a long term rental or purchase).