This is a particular problem and there might be different reasons why this is occuring. This is why you should have indicated the complete error message that has popped up while trying to play that specific music file. For having clear information why this might be happenning, please get here
The file format might also be resulting in such, please indicate the format of the files that you have downloaded, it will be of great importance.
Meanwhile, I will advise you to check and get into the following steps. One of the possibility might be that there is a corrupted or missing library. For this possibility, you should get the WMP closed and then get through this path.
Start> Control Panel> Administrative tools> Services.
Then select Stop after having right clicked on Windows Media Player Network Sharing.
The next step will be deleting CurrentDatabase_***.wmdb and also LocalMLS_*.wmdb which you will find in the Media Player folder. The complete address path is C:\ Users\ Username\ AppData\ Local\ Microsoft\ Media Player. Note that the "Username" is actually yours.
Now start your media sharing service and get the WMP restarted.
Thanks in advance.