Engine will not crank.

Trevor check your grounds both at the battery and on the frame . By the relay are you referring to the relay in the fuse panel or the starter solenoid . When you boost the car to start it are you connected to the battery for your ground or are you on the frame . Just as a test connect the booster cable to the ground(-) post of the battery and the other end of the cable to a solid ground point on the engine block ( don’t worry about the other side of the booster cable were just trying to make a new ground for the battery in this test). If it starts with just the new battery and no boost its probably a bad ground