Today, Hawaiian is written using English letters. I imagine, though, that the language existed in some written form before the native Hawaiians had any contact with English speakers or Western Europeans.
What does the native written Hawaiian language look like, and is the original form now dead?
Before James Cook discovered Hawaii, the language would not have had a written form. It was first written in the early 19th century using the Latin alphabet.
The Hawaiians did not have a written language of their own. Various missionaries and colonists started using Latin letters to write Hawaiian words beginning in the 18th century. Beginning around 1820, a group of missionaries codified a complete system of written Hawaiian using Latin letters, so that they could translate the Bible into Hawaiian, among other things. This is also the time when the King of Hawaii wrote the first written Hawaiian Constitution, using the new system.
To a certain extent, the creation of a written Hawaiian language (using the Latin alphabet) actually changed the language. Originally, the language had a number of sounds that were not found in English. Rather than creating or borrowing characters to represent those sounds, the missionaries represented those sounds with Latin letters. The “Latin” (or “English”) sounds are now frequently associated with the language, particularly among people who use printed texts to help themlearn the language. (There may be native speakers who have preserved the original pronunciation, but I do not have information on that.)
The two clearest examples are the /L/ & /R/ confusion and the /K/ and /T/ confusion. In older works, we can still find references to the city of Honoruru. This is not because someone was attempting to mock the Hawaiians with a fake Japanese accent, but because the original sound was a liquid rather median between an /L/ and a Midwestern /R/ and the language committee chose to impose the /L/ sound. Similarly, there was originally a sound made by placing the middle top surface of the tongue against the middle of the palate. There is no equivalent sound in English (although in some dialects it is the sound of a “clucking” tongue represented by “tsk”). After some debate, the language committee decided that the /K/ sound, made by placing the back of the tongue’s surface against the palate was closer than the /T/ sound made by placing the front of the top of the tongue against the alveolar ridge, so the sound was assigned to the letter K–and since the Hawaiian’s had only the single sound, all references to the /T/ sound are now written as “K” in Hawaiian.