Mail Quits on Mavericks Mail program on my Mac Pro (early 2009) doesn't want to start, or rather just was quitting after I tried to start it multiple times.

I deleted it and tried to re-install old mail program from Snow Leopard disk, now I don't have mail at all. Can anyone help me to deal with the problem?

Important: I installed Mavericks two days before it happened.
If you still have the old backup of the Mail database prior to the 10.9, you can replace the mail folder in ~/Library/ by the old version, and restart the Mail in your Mavericks. The new Mail will convert it to the new version of the database structure. 

I met the same issue a couple of days before, fortunately, I have the Time Machine backup, thus resolved by this way.