Did you check for javascript conflicts? If the menu happens to use javascript to display the custom dropdown/cms block and there is a javascript conflict with the banner slider than this could be causing issue. (and is the most suspect since it is only occurring on the home page.
Also has any xml been modified? It depends on how the static block is being loaded in the menu, but if done the correct way, the block must be refrenced in the xml (most likely app/design/frontend/yourpackage/youtheme/layout/catalog.xml)