Libreoffice can't open .docx files?

I keep trying to open .docx files but get the error “___.docx is not a valid win32 application.”

That is not a LibreOffice problem. Your Windows OS is a little confused.
It is trying to execute a file as if it was an application.

Right click on the doc icon, click on “Open with”, click on “Choose Program”, select LibreOffice from the list (or Browse to C:\Program Files\LibreOffice 3.5\program and select swriter.exe), check the “Always use the selected program to open this kind of file” box and click on OK.