It is okay to eat beef that has turned brown as long as it is still pink on the inside and does not have a foul odor at all, as it is an indication that the meat has gone bad. It is extremely important to properly inspect the meat you are keeping refrigerated before eating it, just so you will be able to make sure it is safe to eat. The fact that the meat in your refrigerator has turned brown simply means that the remaining blood in it has drained out. Although meat may turn brown after just a few days, it is usually still good to eat.
As long as the beef you are storing is not malodorous, it is most likely okay to cook and consume it. You will find that the same thing applies to ground beef; it tends to lose its color much faster than regular meat that has been cut because of the fact that there is more moisture in it. Even if it has a slight odor, you will still be able to cook it. You will just have to make sure that you inspect it carefully to see if the inside is still pink. You can expect the beef you put in your refrigerator to turn brown around five days after it goes in, due to certain chemical changes which occur.