There is nothing wrong with the relay. I would not have started for him if the relay was bad.

Now, the starter is a different story. The battery might not be up to snuff.......even if fully charged.......and the result is a slow turning starter.

Furthermore, any starter that they install will probably be a rebuilt POS that won't last more than two years. A Bosch remanufactured starter is over $140. just for the part and they will get a good two hours for the labor.

So, my advice to you is to go and buy a brand new, group 49 battery from Autozone if your existing battery is older than three years. The investment of $65. will be well worth the expense.