Where did you source the "new" starter? Is the engine a high compression 350/400/455? If so did you purchase the high compression starter or a standard duty unit? Could be the timing as Eric mentioned or the starter has a bad commutator or the copper washer is junk in the solenoid. New doesn't mean good especially with the glut of chineasium junk on our market. If it was me I would take it apart and inspect these items and return it if found faulty.You can disassemble/assemble it carefully so the counter jocky wont deny return if your versed in the starter dissection?