Computer Crashed. iTunes Library Lost. How can I get it back from my iPhone

I have 522 Purchased songs on my iPhone. My computer recently crashed and we got a new hard drive, so all settings were refreshed on my computer. I plugged in my iPhone to transfer my Purchases back to my iTunes library. Again, 522 Purchased songs, and only 303 of them copied. I tried transferring them again, however it didn't transfer anything. Is there anyway I can get the songs back from my iPhone?
Note: My iPhone is on automatic update, and if I try switching it to manual I'm prompted that in order for the change to occur I must Erase and Sync my iPhone which would completely defeat the purpose of my trying to get my music back on my computer so I can put new songs on my iPhone as well.

Purchased songs should be able to be copied back, but if not, maybe you need use other tools. This is a frequently asked question, you can have a look of below answer.
http://discussions.apple.com/message.jspa?messageID=6741373#6741373

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