If I create a non-profit organization, will I be able to have an income ($35,000), or would a salary be considered profit?

Non-profit organizations can, and perhaps most, do pay their employees, officers, and directors.  The shareholders cannot receive a return.  The Green Bay Packers, for example, are a non-profit organization.  The players and management are paid - quite handsomely at that.  If the team were liquidated, the money would go to another non-profit, not to the shareholders.