You need to give more information when you post as it is not immediately clear to which z-index you are talking about.:)
After looking at the code for a while and testing I believe you are talking about the submenu not showing up which has nothing to do with the z-index anyway so you sent us in the wrong direction to start with:)
The submenu is not showing because you have hidden the overflow here:
You will need to remove the overflow:hidden if you want the submenu to pop out. If you were using overflow as a float clearing mechanism then you will need to use one of the other methods as far as the line that contains the nav is concerned (see CSS faq on floats).
Sorry to take you to task for trying to help but negative z-index were not mentioned in the post
Indeed your solution is basically meaningless and has nothing to with how negative (or positive) z-indexes are applied anyway. Finally adding "top:0; left:0; top:0;bottom:0;" is also meaningless as that is the default for a relative element anyway and specifying does nothing at all unless it was to override a previous setting.