Well, you are using a jquery script to change the dropdowns CSS upon hover, which is bad, and as a result this isn't a CSS problem.
I'll request a move into the JS forum.
If you remove t he display:none being given to the dropdowns <ul> it will appear. However, it should be set otherwise in the JS, which makes me think it is that problem.
You should really be using a pure CSS dropdown anyway (with fading effects added on later)...but I digress.