I say good morning, even if I know I won't get a response. I had a former coworker like that. I'd say good morning and she'd rarely respond or if she did it was more like a growl. After she left I learned she was in an abusive marriage and had a hard time trusting people.

I also have a friend who is incredibly shy who tends to ignore people out of her own insecurity. I know she still appreciates those kind efforts and beats herself up for her lack of response.

I'd still greet her if you want to. It's a nice gesture.