Well you say you downloaded Frostwire, and from your post I gather that happened without difficulty. That means that http downloads have no problems being moved from the temporary files after they are finished downloading. This tells me that the corruption is most definitely in part of the Limewire/Frostwire install.

Try uninstalling Limewire and Frostwire and deleting the entire Limewire/frostwire folder in application data.

go to Start->Run type regedit and press enter. navigate to HKEY_LOCAL_MACHINE->Software and delete the Limewire and Frostwire folders.

Download and clean your registry using ccleaner, just in case something was left behind.

Now install one of the programs again and try downloading something.

If your downloads still disappear then the corruption isn't caused by Limewire and you need to start looking at your security programs.