The incomplete folder is a default folder that stores your partially downloaded files. When files are 100% downloaded they are transfered from incomplete folder to your download folder.

Your Desktop is not a safe place to download files to. A virus could easily corrupt your user account & your desktop become a mess.

In past, the default download location was: C:\Documents and Settings\"your account name"\Shared

To change the download location, go to LW's menu bar, Tools > Options > Saving & press Browse button & direct it to wherever you choose to have the download folder. The incomplete folder is always in tandem with the download folder, in same directory or one above.

As for your connection problem, we need more information: System details - help us to help you (click on blue link)