Syncing Apps not working?

[M and M]

My cousin gave me his 32GB Ipod Touch which already had some app and games on it. I bought my own apps on my computer but when I try to sync them it does not work. I go to My Ipod >> Apps >> Sync Apps >> Apply >> Remove. Then my Ipod switches to the "Sync in Progress" screen but once it's finished nothing changed. The old app are still there and the new ones are not.