I imagine that a future with depleted resources would lead to an interesting value system developed around scraps of remaining technology. I imagine that most power plants are down, so electricity isn't really an option for the survivors. Anything that runs on whatever futuristic batteries are still somewhat functional will be worth fighting for. I can picture a band of 30-40 people living in what used to be a hospital waging war on their neighbors to get a generator that can power a machine that provides some sort of life saving cure for their emotional/spiritual leader.
Food will be hard to come by. In our dystopia, I see it coming in two varieties: foraged/farmed, and canned. Obviously, there is a finite amount of canned food around from before things went to hell, so access to it will be important for some communities. If the story is set far enough into the future, I can imagine farmland being closer and closer to unusable as urbanization crawls across the world. Farmland would then be a scarce resource, as would the knowledge, skills, and tool required to use it.
Weapons are the third major resource that I imagine. I can picture a community having access to 12 guns and, say, 375 bullets. They must decide how to use this incredibly limited resource: should they hunt for meat, or save it for defense?
The more I think about this world, the more I wanna read about it. Write me a novel, Zach. Have it on my desk by, say, Thursday?