How do I get all of my itunes purchases to show up on a new computer?

You would have to put them there. You get one download only. it is your responsibility to copy/move/backup your purchases.

Use your backup copy of your computer ( files/music/pics/docs/etc) to move the music to your new computer.

If for some reason you have failed to maintain a backup ( not good), then you can transfer itunes purchases from an ipod: File>Transfer Purchases

Put the old computer's hard drive into an enclosure and copy the files off, use the Transfer Purchases function in iTunes if they're on an iPod or similar Apple device, or click here and ask.

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I'm sorry for piggy-backing on this topic, but I don't have any other link by which to post my question. Anyhow, I purchased a new computer and installed Itunes, signed in, and found that ALL of my music, both purchased and imported, was completely missing. I then checked the Itunes program on the other computer that was replaced and found that the music on that computer was missing also. Can anyone help, please? Come on, Apple, these constant problems are getting really old and tiring.

Problem sorted