I can't figure out why it's transparent. I have it set to display as shaded with edges.
Are you sure it's not set to transparency on?
How do I check that? It's not under the menu of shaded with edges, shaded, hidden lines visible, wireframe etc.
Actually I found it.
Did it fix the problem?
If so, mark the question as answered by Craig's answer.
If RMB the part that is transparent without anything behind it it will select that part and the popup window will let you change it.
Are you sure it's not set to transparency on?