The problem with Apple is that they make everything use a propriety format so it's difficult to make them work on non-Apple products. If you bought the songs from iTunes back in the days when they were encrypted with DRM then they will only play on Apple players. You may be able to upgrade some of these to the "Plus" format which would then work on any player capable of playing Apple's .aac format, but you will have to pay for the privilege - it's a sad situation to be in and it's why I refuse to buy anything from Apple - these sort of strategies are normal throughout their entire product range!
If you purchase any songs online in the future, may I suggest you try Amazon MP3. Music is generally cheaper than on iTunes, plus they are encoded in the almost universal MP3 format.