If the transport proteins that carry amino acids into a cell stopped working, how might the process affect the cell

the cell would cease to function and possibly die. Proteins are used for cellular repairing and chemical processes. Ribosomes are one of the most important organelles in the cell, mostly part of the rough endoplasmic reticulum. It manufactures enzymes such as proteins which will be utilized by many organelles in the cell. Microtubules are one, responsible for the framework and acts as a skeleton of the cell –cytoskeleton needs proteins, also cytoplasm and other organelles of the cell. For a prokaryote or a eukaryote cell to survive, they need protein. 

Cell would likely die because it would no longer be able to reieve the amino acids