What would be the path of the moon if somehow all gravitational forces on it vanished to zero?

The Moon would take off in a straight line, at a constant speed, with the

same speed and direction it had at the instant that gravity got switched off.

(Of course, if ALL gravity got switched off, then the Moon would fall apart.

The radioactive and volcanic heat activity in its core would continue, and

suddenly there wouldn't be anything to hold it together. Same for the Earth.)