right, the atoms remain behind even though the chemical bonds re-arrange. Most decomposition will leave some solid residue, but it depends on what is decomposing. If it is a pure carbohydrate, for example, the atoms left behind are all gases, and would float away, leaving no solid trace.
Total decomposition of vertebrate animals will also take a very long time Please Register or Log in to view the hidden image!
In practice, the decomposition of organic matter is greatly accelerated by detritivores, other organisms that consume the dead tissue, metabolize it, and convert it into something that can be readily used as a resource by a living plant, animal or other organism. Lignin, the substance that makes wood so hard and sturdy, is one of the most durable organic compounds. Certain species of fungi have evolved the enzyme required to decompose it into simpler materials. Without them, dead trees would just lie around, hoarding all that precious carbon, for eons.
Organic matter is high-energy stuff. They are decomposed by bacteria and used as energy sources. Dead bodies literally become food for the little buggers. When utilized as energy sources, they undergo "biochemical redox reactions". In order to extract the energy, organic molecules have to be oxidized. So organic carbon matter is converted to carbon dioxide. Hydrogen is converted to water (or protons in acids). Organic nitrogen is converted into nitrous or nitric oxide. Sulfur compounds into sulfates. Trace metals into their metal oxides, etc. The same end result is obtained when you burn (combustion is essentially a redox reaction) the organic matter. The bacteria can be said to be burning the organic matter, albeit in a very controlled manner.
Will it leave a trace? By that, I understand you to mean that if you took some dust or random material off the ground, can you tell whether it came from a dead body or not? That's hard to answer. Technically, no. It's impossible to tag each molecule with information to say it came from a dead dinosaur or some such. If you wait long enough and break a dead body down into its constituent elements, nothing will be left to indicate that it was actually part of a living organism previously.