Slow to turn over. If starter is going will I get a service engine soon light?

Hello, the starter motor has absolutely no relationship to any warning lights. It may or many not be a starter concern; always start by testing the battery to ensure it is fully charged and able to sustain a load. Good shops have great test equipment for batteries. Additionally, check further your battery cables and all connections - corrosion can cause a voltage / amperage drop as well. A starter motor failure is almost always a "guess" unless you can measure drawn amperage with test equipment. And that can be an expensive guess! So, good luck.