Do you know what an incomplete file is???? It is a partial downld. So if you start downlding a file, a file is created within the incomplete folder of that name which gradually increases in size as you continue the downld. Once it reaches 100% downlded & LW has verified it as agreeing with the original downld hash tree that was downlded then LW will then move it to your downld folder (aka Shared folder.) But I can't believe you're so silly as to downld to your desktop!!! You really are looking for trouble with your system by doing so. If you should downld a virus by mistake then your system/user account is "stuffed!" At least keeping it within the default location which is C:\Documents and Settings\"your account name"\Shared
then you can isolate it. I would recommend going to your LW preferences ie: go to LW's menu bar, Tools>Options>Saving & press the Default button & press the apply button.

You can't delete a file that is being used. And either that incomplete file is being used by LW as it is still downlding to it or else it is being shared by LW.

BTW if you want quick access to your LW downld folder then either create a shortcut to the desktop for it or else: Go to your LW Library window, select Saved Files folder & press the Explore button. Sample image here: Using Library Explore button to access downld folder (click on link)