If you will see on firefox or chrome then, it works fine. You can see background Image on search engine but, same doesn't work on IE8. Background Image doesn't comes on Search engine. However, it works fine on localhost in IE8 also.
If I will remove my background color then, if the document size increase vertically, then, bacground becomes white. Kindly, give me some alternative solution. Note:- Z-index is working fine for IE8 on localhost, the issue is only for live server.
Now, it's working. You can cross check on IE8. Just I commented 'position:relative' from both div i.e. #left_search & #main_search and it started working. I don't know why position:relative was conflicting. Any way thanks for your help. You can find css below:-