Moving Blog – How to transfer?

I purchased a wordpress blog from a friend and am trying to transfer it to my own server. He sent me all the ftp files under public_html, and gave me a mysql file from phpmyadmin. I have uploaded all the ftp files, created a mysql database and user (and assigned together), and restored the mysql file. Now wordpress tells me that it seems that wordpress isn’t installed yet, and asks me to install again :S. I tried installing again, and it just started new. How to a restore my backup files?