If these songs no longer play on your PC either, but worked fine when you first downloaded them, it is likely that they were actually WMA songs with DRM restrictions. For example, some artists allow users to download full tracks to promote their latest singles and albums, but these are often limited to a few playbacks or expire after a certain date. Generally promotional DRM protected songs cannot be transferred to any player, even if the player has DRM support and the songs have not yet expired.
Another possibility is that the songs you have downloaded are in a different format to what your portable player supports. For example, if the songs you have are actually Wave files, you'll need to convert them to MP3 or WMA before you can play them on your handheld player. To see if this is the case, try downloading an audio conversion utility (see Wikipedia for a few here) and convert the song to MP3 to see if it will play.
If the songs have never been able to play, try checking the size of them by right-clicking on a non-working song and click "Properties". If the file size is a few KB in size, it is a failed download. If the song is 2MB or larger, then you likely have the song, but either your PC is missing the codec to play it or the song is DRM protected, but not authorised to play on your PC.