What you describe suggests that one or more "lock" files have been left behind from a previous Word session. These files, also called owner files, have names starting with ~$ and the remainder of the name is identical to the original file name. For assistance with locating and deleting the files, take a look at
http://www.gmayor.com/what_to_do_when_word_crashes.htm.
For more on temporary files in general, see the Knowledge Base article at
http://support.microsoft.com/kb/211632/en-us.