Place potatoes in a microwave-safe bowl and add water to cover. Add corn. Cook in the microwave on high for 5 minutes and stir. Microwave 5 minutes more. Drain.
Heat olive oil in a saucepan over medium heat. Add garlic; pour in potatoes and corn and stir until coated in oil. Mix in garlic powder, salt, chili powder, oregano, marjoram, paprika, cinnamon, and black pepper. Cook until potatoes are soft and browned on the outside, about 10 minutes. Add ham; cover and cook until ham is heated through, 5 to 10 minutes.