Anyone have any thoughts?? Please!!

There is no magic solution that ignores the realities of electricity. You nixed the only real solution. You need to get in an electrician and have him do direct wire LED to a switch. 1-2K, depending on the routing of the wiring.

What is it you want to illuminate? We have a built in bookcase in our family room without lighting (although we do have an outlet so could add it) - we have track lighting on the ceiling aimed at the bookshelf and it works quite well. We can aim it as we like. It's white track lighting on a white ceiling so it fades away as all but a lighting source.

If you are just looking for a nice ambiance and not trying to light specific things, you could do battery-operated "candle" light.

See these pictures to see what I mean ... 4 track lights aimed at built-in. I actually like the lighting better than the in-cabinet lighting I have in other pieces of furniture.