What should I do if I’m denied a raise at work?

First find another better paying job and then quit. Until you get another job, keep working with the same level of dedication. In short be a professional. In any case, do not quit out of frustration before finding another job. And once you do get a job, and the existing company decides to give you a better offer, politely decline and move on. You had given them a fair chance earlier and they didn’t take it. You will only lose your respect if you accept it. But don’t leave on a bitter note, you never know if destiny brings you back to the same company or you meet your boss in another company.