According to Wikitravel, unless your car is amphibious (like the Aquada), you'll need to get it freighted to Hawaii.
Fortunately this seems fairly common, and a quick google search gives a few results, including this on Hawaii Car Shipping:
According to them it usually takes three to four weeks, you will need a variety of paperwork and (of course) shipping insurance. But it's certainly possible.
However, you won't be driving WITH it. It'll be being shipped. So that depends on your technicality rules for your challenge.
Unfortunately, as per the same Wikitravel link, the days when everyone arrived by boat are gone. The only way you can get there yourself by boat is by cruise ship from the western coast of North America, for example, and I'm not sure if any companies allow you to bring your own car, let along drive it onto the boat...