First of all, you do not want to surround your map with a hollow box...that will kill your rendering speeds.
2nd, your map might be fullbright because you do not have any lights in your map yet. Are you using Zoners compiling tools or the one s that came bundled with Hammer? If you are using the HAmmer ones, amy God have mercy on your soul, go get Zoners! I dont know the exact link, but look up ZHLT in the forums search here in THWL or in Google