If you aren't getting a Music heading under the Purchased link under on the right-hand side of the iTunes store homepage then what country are you in ? Music can't currently be re-downloaded in all countries.
What content types can be re-downloaded where : http://support.apple.com/kb/HT5085
If you aren't in a country where you can re-download music then you will need to copy it from your old computer (copying music between computers) or your backup and add it to your Mac's iTunes library via File > Add To Library.
If they are still on your iPhone and/or iPad then you could also copy them over from them via File > Devices > Transfer Purchases, though you may also need to read there 2 user-tips helpful :
syncing to a new computer : https://discussions.apple.com/docs/DOC-3141
recovering content from a device (e.g. music copied from CDs) : https://discussions.apple.com/docs/DOC-3991