Can you guys help me calculate the kinetic energy of a ball that was given an impulse?

The problem states that "an impulse J is given to it". As impulse is the change in momentum, I think you're right to ignore the "free" rotation. (There is an implied friction at the surface to create the rotation given that the impulse is through the CoM). So I would say v=J/m and add up the k.e for linear and rotation from there.