Yes, more info is needed. When you move the files from one folder to another, do you drag and drop? Copy and paste? Use the cp command? Use the mv command? Which folders are you using? Are you using right or left mouse click?
Have you tried mplayer? VLC? Clementine?
Use this command to open one this isn't playing in a terminal:
smplayer /home/<your-user-name>/<your-folder-name>/song-name.extension
Use the full path to your song, please. Post any output.
First of all....I have been up for 2 hours working on this.

Just want you to know I don't post for help without first exploring on my own. I had written a long long write up yesterday and wrote another one this morning trying desperately to explain what is happening without weaving a coat of many colors.
I think I have solved it but time will tell.

I have the full install of LXDE on an alternate partition. I booted there today to see what happened. I copied the offending folders over from the KDE. A similar thing happened. I could play the wav files with Clementine but not with MPlayer. Yet if I copied the wav file ..say to the desktop, it would play with both.
I did this same trial with different folders where I have wav file or even music files not of my making. I knew the folders contained similar things and were made at various times. But the dates did not seem to matter. Some folders were made years ago. Some recently.
I looked at 2 folders that had the same name except for being called XXX_1 and XXX_2. One would play and one wouldn't.
Upon looking closer I saw this
XX X_1 and XXX_2. I went back and renamed closing up the spaces.
I went to several other folders that I had left spaces in the names. I renamed with no spaces and now it seems I can play any wav in them with both players.
Who knows?

When I boot back into my main KDE install I will check the newly named and see if the smplayer is now working.
Right now I am staying in the LXDE install. (I like it....

)