Tried moving the box, and well away from the Dish box. Still issues. As soon as I unplug the Roku, the Dish remote and box work great. When I turn the Roku back on, the Dish remote won't respond at all, unless I'm 2 inches from the box. Roku is going back if this is the case.
The Roku box doesn't emit IR, so this is a strange problem. There have been a number of cases where the backlight from the TV interfered with the ROKU remote, giving the same results you are seeing with the Dish box. How do you have the Roku connected to the TV? It should be connected directly, not through the Dish box.