Elements and carbon
Carbon skeletons can be chains, branches, or rings. Functional groups change how those skeletons interact with water and other molecules: hydroxyl groups are polar, carboxyl groups can donate H+, and amino groups can accept H+ under appropriate conditions. Biological function depends on atom arrangement, not just an element count. Organisms obtain atoms from their environment and rearrange them through chemical reactions; they do not manufacture carbon atoms when they grow. Nitrogen availability can limit protein and nucleotide production, while phosphorus availability can limit nucleotide and phospholipid production.
A plant supplied with light, water, and CO2 can still fail to grow normally if usable nitrogen is absent. Carbon fixation supplies carbon skeletons; it does not supply the nitrogen needed to make amino acids.
Carbon is not an energy source simply because it is carbon. Energy changes depend on the complete reaction and its reactants and products.