Keep in mind there is no standard for HDTVs in reading these types of files. Also, you should be aware that .MOV/.mov (capital does not matter) is only a container. The codec (h.264, Sorenson) etc.) used to create the file was made is where the rubber hits the road. If the 7D doesn't use the same codec/compression scheme that the Sharp requires, it still won't be able to read that particular .MOV file. In this sense, you should convert it to something you know works well already.
The following site should help:
Thanks for your help, my new Sharp LC52LE640U tv will read a usb mem stick with .mkv files, but not a .MOV file from my Canon 7D? .mov files are listed as acceptable in the Sharp manual. Do I need to convert to another video format, or should it be a .mov extension rather than .MOV . . . (can't be a problem with capitals!?). Thanks again! Peter