How do I add ambient light to a picture?

I’m trying to make an indoor room scene. Here is what it looks like:

How do I make it so the back wall is illuminated? The room is lit by a area light outside the window, to simulate sunlight. I have tried the global ambient color, which seems to make the entire picture be “washed out” with a gray color.
Any help? I have a feeling this question is n00by, but I can’t think of any way to solve this problem.

Give the back wall it’s own material, then give it an exclusive light group, put the back wall on it’s own layer, give that layer a light and set the light to layer only, use a shadeless blend texture for only that wall’s material to fake a light, etc… There are really a hundred or so ways to go about your task and there’s no real right or wrong way of doing it.

even simpler, put a lower powered point lamp inside to room (where the area light is illuminating the floor) to fake “bounce” light. make it the same color as the floor to get a very simple GI fake.