You don't need any miles in your account to search for awards. If you try to book an award ticket without sufficient miles in your account, it will prompt you to buy the required miles.
Make sure you are only searching between airports that HA flies to themselves. You cannot use the HA website to book award tickets involving JetBlue flights or other partner airlines.
Make sure you are still actively logged into your HawaiianMiles account when you try to do the search. If you log in and don't click anything for a while, your session can expire. This can lead to the "Miles" radio button in the search disappearing or not working.
If you've checked both of the above, then it's possible there is no award availability for the dates you're searching.