z-index only applies to positioned elements. Therefore if the element is static then you need to add position:relative (without co-ordinates) and then you can apply a z-index as required.
This has no visual effect on the element other than providing a stacking context for positioned children and to also allow a z-index to take effect.
(Note that in IE7 and under its ultimately the positioned parent that controls the stacking level (contrary to the specs as positioned elements should be applied z-index auto by default but IE7 and under applies zero) so its no use increasing the z-index of a child of a positioned parent because it will have no effect outside its current context. It's the parent z-index that will control the stacking level with regards to elements outside the current context. )