Suppose that a patient is diagnosed with new disease caused by build up by the waste material in the body's cells which organelle is most likely malfunctioning in patients cells

The answer to this question would be lysosome.

Build up of waste material mostly caused by disease in the enzyme that digests the material. Lysosome would be the organ that will hold the material until it was digested. Since it won't digest, the material will be in lysosome forever. The disease itself called lysosomal storage disorder, which was part of the inborn error of metabolism.