The paper products are okay if you have plenty of "greens" to go with them. It's the balance that its key. But it does sound like you are definitely short on greens. You talked about the critters getting the kitchen scraps. Is your pile not enclosed? My compost bin is about like this:wire bin composter
but also has wire grid across the top of it. The main point of it, as well as keeping the pile piled, is to keep the critters out. Without it, kitchen scraps would never stay in my pile long enough to compost, either.
You mention the grass clippings, but what about other yard waste: pulled weeds, deadheaded flowers, trimmings, thinings, etc. My yard generates tons of greens during the season... Are you not putting all that in the pile?
And you mentioned dry. Moisture is very important. As soon as your pile dries out, it STOPS working. Every time I water anything in the yard, I water my compost pile thoroughly AND it is where it can get rained on and open to the rain.
No, not the pine needles, they break down very slowly, won't help your situation.