Recently downloaded music on my iPhone 4 from iTunes won't play. What do I do?

Just yesterday, I downloaded four songs from iTunes at my cousin's house. They live on a hill and their internet isn't really the best. I've noticed that music I usually download using their Wi-Fi tends to have issues.
What happens is that I click on the music I've downloaded, but it just doesn't play. It doesn't skip the song or anything like that, it just stays there, at 00:00. I would also like to note that it seems as if it didn't fully download properly because the cover photo for the song isn't showing up.
I've tried restarting my phone and re-downloading the music, but nothing seems to work. I've considered restoring my iPhone, but I have hundreds of apps, music, photos, contacts, data, etc. That I'm not willing to have to redo.
If any of you have a solution other than restoring, that would be wonderful!

You can redownload your puchases.

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