Molecular nanotechnology was popularized and proved by the monograph: Engines of Creation, by Eric K. Drexler.[1] Molecular computers involve the storage and processing of data at the molecular level.
The obvious existence proof provided by Drexler was the processing and storage of data by DNA and other biomolecules in living systems. DNA code data using 4 molecular letters, A, C, G and T. This makes DNA a base 4 storage device. It has error control hardware, and the abillity to make copies of itself. Viruses are able to edit DNA to their own ends.
Nanotubes made of tubular graphite sheets have been used as conductors and as transistors in experimental molecule sized computational devices.