I apoloize if this is too obvious, but in my learning Maya, even though it's simple has happened to me alot since Im getting used to all the hotkeys and navigation. But are you sure you are hitting the "snap to grid" hotkey BEFORE you click the mouse button to drag the items in order to stap them? It's just a bad habit I have of selecting the object to drag and then clicking the snap hotkey and of course it won't read it. So I have to unclick, press the hotkey, then click the object to drag it again. Anyway, hopefully it's that simple of a solution for you. 
