Jon, it worked! Thank-you, thank-you, thank-you. Now my problems are ALL solved. ;-)

I have mplayer.exe and mplayer2.exe. I went to mplayer2/view/options/format and checked the block for midi. Now it works!

I can only guess that when I downloaded RealAudio or Winamp it scarfed up this designation. Then when I uninstalled them, there was nothing to open midi files with. (even though in the associations dialog that Malcolm directed me to, I associated midi files with mplayer. Oh well, it works, so I'm happy even though I don't understand it.