when you say the files are from "Mini-Disc recordings", do you mean they are from a Sony Mini-Disc player? so are the files in ATRAC format then? (oma/omg)
but anyway, about your dct files, it is very odd that the other computer cannot read dct files, because the codec should be installed with windows by default. What windows version does the other computer use? Note that .dct files are not playable in Media Player because the format is our own. You can only play it using our software.