With that out of the way, I have a problem. In my map, there is a small box under the floor to hold a panel arm. When I check it in game, the bottom of the box is all black, even though I have lights nearby. I tried putting a light inside the box, but it didn't change anything. I've searched the web to no avail. Help?

1) your texture is missing, you can see it in the texture browser, but you can't use it.
Try a different one

2) your light Is not near enough
Add one under it

3)there's a leak
Find it to fix it

4)if these don't work upload the wmf file for me to see

That might be it, I seem to remember somethingf about lights not working if they're too close to stuff.

No, no leak.

Here: http://dl.dropbox.com/u/6478970/BennettChamber-5.vmf

Though I didn't use vis and light when compiling in expert mode
Try typing
"mat_fullbright 1" in console when testing the map