Background images in list items not showing in IE7

Question

What is it that I am not understanding about IE7 and background images in list items? I'd like to understand this once and for all please because I run into this problem a lot and only get it right with severe hacking.

Please take a look at this link, the link menu items in the left and right column are not showing and I am not sure what to do to fix this.

If I say display: inline-block on the li, the the background image shows but is off completely. I'd like to just understand this so that I don't have to struggle with it again please.

http://tiny.cc/pspb7

Thanks all!