Issues with any updates, downloads or add-ons. Nothing will work.

When I try to save any files, download any content the download box will pop up and my file will show there but when I try finding it in the files or opening anything up it says "Shortcut not found" also when I try to install Flash or any plugins they fail. The agreement page won't even show. For example, if I go on Google Images and I click save as on a file, say download to desktop the download box will appear, it'll say download complete and it will not be on my desktop. I've searched in every nook and cranny and tried saving to different files so I know that's not the issue. Is there something I'm missing? I never had these issues in any previous downloads of Firefox on other computers.