IOS 7 doesn't play most of my songs?

I recently updated my iPhone 4S to IOS7 and since then my phone has stopped playing about 80% of my songs! They just appear as grey squares! I went to the apple shop and they told me to do a factory restore and then update my contacts etc from iCloud, I have done that twice and still once the songs are synced onto my iPhone it refuses to play most of them! Anyone know what else can be done in this situation?

I'm not guaranteeing this will fix it, but I have had a similar problem in the past related to music not playing on my iPod Classic 120GB, where the music appearesd in the menu, but it simply skipped to a track it could play.

- Connect your iPhone to your PC, load up iTunes.

- When it appears click (your name's) iPhone on the sidebar. If you don't see a sidebar where it has Music, Film, TV Programmes etc… Press CTRL+S to bring it back.

- Now where it says "Manually Manage Music and Videos", make sure this is ticked.

- Hopefully, the music that you had on your phone should be on your PC too. If it isn't, either sign in to your Apple ID and it will download them, or you can use SharePod to transfer them back to your PC.

- Once you've got them on your PC in one form or another, and the music plays OK, delete the music that is on your iPhone.

- Now find those songs, and click and drag them onto where it says (Your Name's) iPhone and the music should synchronize back over.

- Once this is done, hit the eject button to safely disconnect your iPhone.

Now, see if the music plays.