The search scroll bar shows for me with LW 4.18.8 on Windows XP with Java 7.

The suggestion about the deleting of the preferences folder will not guarantee it will fix the issue for you. But if you are using the same preferences from LW 5, then this may have affected how your LW 4 behaves. Having said that, I'm using the same preferences from having used LW 5 on a previous install but I am not seeing your problem. These kinds of quirky bugs are usually restricted to specific users on their particular system. If not confident about the deletion of the preferences folder then backup the entire folder before deleting it. If deleting it fixes the issues great. If not and you'd prefer to go back to the older preferences folder then do that.

I cannot remember if I did my sample image of deleting the LW preferences folder using Windows 2000 or XP, perhaps the previous. But it is the same principle. Keep in mind different XP machines can look a little different depending on how their view system is set, classic or ... cannot remember now.