How to put music on my iPhone 4 using a different computer?

I have an iPhone 4 and i backed up my phone and added music on with my dads laptop but i recently got a desktop computer and i backed up my things there to but for some reason i can't seem to put music on it and i don't know why, like it doesn't give me the option to add music. If anyone can help me or tell me why its doing this it would be great. I have the new version of iTunes and still nothing. Please some one help & thank you in advance!

Just download it.

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