If you book your room through Member Services you would get free Internet. However, because you have free dining, it appears that you booked through Disney Reservations, which means you will not receive free Internet.
If you book cash nights through MS at a DVC resort, your stay should be just like a points stay. If you book the cash nights through Disney Reservation Center, you get treated like any other person purchasing a reservation directly from Disney - daily housekeeping, no free internet, dining plan if you booked under that plan.