Usually this occurs if you have removed one or more Office applications to somewhere other than /Applications/Microsoft Office 2004. Put Word, Excel, PowerPoint or Entourage back in to that folder, and try reopening the affected application. If this doesn't resolve the issue you may have to remove and reinstall the entire Office suite.
Are you running LIon? If so, then you can expect Office 2004 not to run because Office 2004 is a PPC-based suite. Because Lion does not include Rosetta, Office 2004 cannot run under Lion. If your computer runs Snow Leopard or an older Mac, then you need to install Office from the distribution DVD.