[The_Neglected]

it's not that deathnote user dont go to heaven or hell when they die. Ryuuku stated in chapter 107 that "Deathnote users shouldn't worry about going to Heaven or Hell" because "Heaven and Hell does not exist. In the afterlife, whatever you've done in your life, you will still go to the same place. Death is Equal."

Therefore, when you die, whether you are a deathnote user or not, you go no where. Your death is the end of the line.

Also you asked if they didnt go to heaven or hell doesn't that mean that they go to the shinigami realm and become a shinigami?

Spoiler: If what you said was true...

then Yagami Light would become what he always wanted, to become a god. With that power he would then kill Near and everyone else that worked with Near. But then L and Near would become Shinigami because the moment they touched the notebook, they became Deathnote users. So if L became a Shinigami, Light would have been killed in a couple of days.

Did that help you any?