Three things I can think of: (1) you have a conflicting keybind preventing R from activating sprint properly, or (2) your keyboard simply doesn't allow all those keys to be pressed at the same time, or (3) drivers.
(1) Check Options > Controls and look at the sprint keybind. If it is white then you have no conflicts (unless you're playing with mods and a mod's keybinds are in another menu). If it is orange or red then there is another action also bound to R. You'll have to remove one of them for the other to function correctly.
(2) Try a different keyboard.
(3) Since you have a keyboard designed for gaming it's possible that you need to install special software or drivers. Many driver updater and installation "assistants" are simply adware/malware, so be sure to get the drivers from an included CD or the manufacturer's website. Head to a reputable tech site like HowToGeek if you need help installing them.
If none of those worked, you'll need to use a different key (or mouse button if you have spares) for sprint, or go old-school and simply double-tap W.