Q: How to retreive purchase music after computer crash lost in back up.  How to restore the music?

Hello Boogiec522,

Thank you for using Apple Support Communities!

It sounds like you would like to download your iTunes Store purchases again to your desktop computer.

No worries there, you can re download them free of charge from the iTunes Store with this article:

iTunes 11 for Mac: Download previous purchases from the iTunes Store

http://support.apple.com/kb/PH12283

Download previous iTunes Store purchases to an authorized computer

1. Click iTunes Store near the top of the iTunes window.
2. Click the Purchased link at the right of the iTunes Store homepage (below Quick Links).
3. In the page that appears, select a category.iTunes shows you which of your purchases are available for download. You can view all of your past purchases, or just the ones not currently in your iTunes library. Items already in your library aren’t available for download.If you select Music, you can view your purchases by song, artist, or album. If you’re viewing by album, click an album to see which songs on it are available for downloading.To search for an item, type its name or a keyword in the search field, and then press the Return key to view your search results.
4. To download an item, click its Download button .To download all available items, click Download All.

All the best,

Sterling