Can't sync music on iPad?

So I realised today that I couldn't add new songs or play some of my already existing songs on my iPad (using iTunes) so I tried to remove the entire music library, and sync it again. But when I removed it, I couldn't sync it back?!

The weird thing is, it actually shows (on iTunes) the songs that I had before I removed them on my iPad, but I can't play it. It shows, I can click on them, but it just doesn't play. I don't know why it still shows when I actually have like 9GB free because I removed my music from my iPad, and it actually says so on settings, but I just can't resync my songs.

I also tried to add music manually, and this pops up:

iTunes cannot add any songs to the iPad because no songs in your iTunes library can be copied to this iPad.

I have no idea what's wrong and I'm really confused. Please help!

Extra info:

My iPad isn't really new, it's half a year old already.

I don't think it's a problem with iTunes because it syncs with my iPod just fine. Or am I missing something?

Other apps sync without problems with my iPad.