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Without deleting all of the apps/ songs on my iPhone?

What kind of computer was the phone syncing to previously? Either way... the absolute painless way to do it is to copy the iTunes folder from your old computer to your new computer. Then when opening iTunes, hold the "option" key and then choose the Itunes Library (.itl file) from the iTunes folder you copied over. Then when you sync your iPhone, it won't erase anything because it is the same Library as before.
 
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