Q: how can i download a previous purchase to my new computer? I can't find it in my purchased category but they appear as purchased on th ei tune store??

What type of item is it ? What you can re-download will show under the Purchased link under Quick Links on the right-hand side of the iTunes store home page on your computer's iTunes. As long as they are still in the store then your apps and ibooks should appear there, and potentially music, films and tv shows (media can't be re-downloaded in all countries) - audiobooks and ringtones are currently one-time only downloads, so they won't appear.

If they don't show then have you still got copies of the items somewhere e.g. on your old computer (copying between computers) or on a backup of your downloads ?