What can be wrong if a car turns over slowly before starting?

Could be poor cable connections. Check black ground and red positive, may need to remove and clean both ends. Lead on battery end can be cleaned with wire brush, knife or sandpaper, cable going into end can be scraped with knife.

But it's usually old or dying battery (starting takes a lot of power.) Don't replace starter or other parts if battery's old or shows problems. Testers availabe at auto supply stores, or they can test it.