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Japan DID invade New Guinea during WWII.
The Battle of Kokoda was a major engagement during that invasion.
If the questioner means what would have happened had Japan invaded and conquered New
Guinea then the answer is "not much."

While holding New Guinea would have allowed the Japanese to more easily target Northern Australia, it would have done little to prevent the US intervention in the Pacific campaign which led to the end of Japan's aggression. New Guinea is 25% larger than the US state of Texas and its rough terrain would have required at least 250k worth of Japanese forces (which they didn't have available) to hold the entire land mass.

If Japan had succeeded in New Guinea, they would have been forced to take troops from China, Formosa, Burma or Korea to maintain it. There's also the fact that while Papua New Guinea and Papua ( the two political entities which comprise the island) are rich in natural resources, Japan's overextension of its military forces and its lack of access to markets during the war would have made any such occupation more costly than it was worth.

By the time of Kokoda (Fall of 1942) and the later Battle Buna-Gona in early 1943, Japan was already suffering from its multiple losses at Coral Sea and Midway. Taking New Guinea would have done little except tie up forces and allow the Allies to isolate those forces there with a combination of air strikes and submarine warfare.