I just finished doing this myself. Mine was already done and working when I saw this post, but I had a look at the instructions mentioned here and that seems to be basically what I did, with one exception.

I found that after moving the database, the site files, and editing mainfile.php, it still didn't work. I fiddled with the paths in mainfile, thinking that was the problem, and I continued to get either an error page or a blank page.

My solution was to run the install again, using the same directory, database, and credentials. I had previously deleted the install directory, so had to upload it to the new server before I could run it. But after running the install, it fixed whatever was wrong and the site now works perfectly. I'm not sure what change it made that mattered, because as far as I can see, the mainfile looks the same as when I manually edited it. However, instead of spending time chasing something that's no longer a problem, I'm satisfied that this worked.

If you use this method, remember to delete the install directory again when you're done.