music won't play offline ~ and I don't want to use cellular data

A few weeks ago, I had to have my windows computer repaired, and the person repairing it had to rename it. ITunes didn't recognize the computer so I had to authorize it to sync music to my iphone 5. I had to go through this process of removing all the music from my phone and putting all the music from the computer's library onto my phone. I didn't mind, because the computer had all the music I've ever bought. Most of my music will play, but some songs, songs that I bought through ITunes, will not play offline. If I click on them, it gives me the option of allowing them to play by enabling cellular playback, but that uses up data. How can I resolve this? I've tried downloading the said songs, but they won't download. They will only play when wifi is working.