In real life a single light source can illuminate an entire room. The reason this happens is because the light bounces around. This effect is called radiosity.
You've got two options. You can either fake it by adding small lights all over or you can enable radiosity and turn up the number of bounces.
The only downside to using radiosity is it slows down your renders trememdously. Also, the more bounces the longer it takes to render.
The above image is an example of increasing the number of bounces.