I don't use Indesign in Windows, but I do on a Mac, and this may be helpful. On the Mac side, Indesign looks first for fonts in a folder called "Document Fonts" located in the same location as your .indd file, BUT that Document Fonts folder needs to have an Adobe font cache file in it too. These cache files are small files called AdobeFntXX.lst, where XX can be any number, like AdobeFnt13.lst. So if you copied your Indesign file to a different identical computer but didn't copy it's Document Fonts folder with it, it is possible the file will have no issues on the first computer, but have font missing errors on computer #2.
Hope this helps.