Beef jerky and salted/tinned fish.
Butter.
Eggs (unopened; only if not pasteurized/cleaned which you will not find in a typical US grocer for anyone other than OP).
Pretty much any baked goods.
Pasta (uncooked obviously).
Avocado, onion, tomato... Pretty much any fruit or veggie that isn't kept refrigerated at the store really.
Nuts.
Chocolate
Marshmallows
Graham crackers
Edit: NO FIRE?! The hell you camping?! Could you at least get some sterno or an electric camping stove? How you gonna have a camping trip without s'mores? ๐ฉ
Although I also would suggest a basic ass ice chest. My family went camping all the time for that length of time when I was growing up and we would bring regular food to cook over a portable electric stove and keep it in an ice chest. It would keep for at least 5 days.