Seeing as how you installed a new starter... I assume a brand new starter, not a used or rebuilt one... I am ruling out a possible defective starter and/or a greased sticking bendix drive. Never grease the bendix as that collects dirt and grime that leads to sticking.
Normally caused by either a loose or a tight but dirty connection somewhere in the starter circuit or a cable that is failing/corroding internally.
Remove and clean thoroughly all cables/wires associated with the starter circuit, including the battery terminals themselves and the ground at the powerhead. Be sure to also clean the component that the cables/wires attach to.
If after performing the above process, the starter still turns slow, feel the cables with your hands for hot spots that would reveal that the cable is failing internally.