Can I fight a claim against me if the other person was parked on a sidewalk?

You can fight anything but I am sorry to tell you that you will loose anyway. The way it is looked at is that if you are moving and the other vehicle is parked you are the only one that can avoid the accident and therefor are At Fault. I have seen cases where someone stops in the middle of the road at night with no lights on and when another car hits them they are at fault. It doesn't sound right but that's the way it is.