Due to nucleic acid’s programmability, it is possible to realize DNA structures with computing functions, and thus a new generation of molecular computers is evolving to solve biological and medical problems. There is evidence that genetic heredity diseases and cancer can be the result of genetic heterogeneity, thus there is a need for diagnostics and therapeutic tools with multiplex and smart components to compute all the molecular drivers. DNA molecular computers mimics electronic computers by programming synthetic nucleic acids to perform similarly to central processing units. Considering how the evolution of integrated circuits made possible the revolution of silicon-based computers, integrated DNA molecular circuits can be developed to allow modular designing and scale to complex DNA nano-processors. This dissertation covers the development of four-way junction (4J) DNA logic gates that can be wired to result in functionally complete gates, and their immobilization on a modular DNA board that serves as a scaffold for logic gate integration, fast signal processing, and cascading. Connecting 4J DNA logic gates YES and NOT resulted in OR, NAND, and IMPLY logic circuits; the three circuits can operate under the input of miRNAs, either oncogenic or/and tumor-suppressors, and give two possible diagnoses: healthy or cancerous. The DNA board can expand as the DNA circuit grows in the number of integrated 4J units. Signal propagation across a wired of 4J YES logic gates showed signal completion in < 3 min, accounting for a signal propagation rate of 4.5 nm/min and that up to 6 units can be cascaded before the signal dissipates. Lastly, an approach to chemically ligate all oligonucleotide components of the DNA molecular device is presented, in which we also found a route for the bioconjugation of 5’ to 5’ and 3’ to 3’ oligonucleotides.