I tried installing the domain mapping plugin for my sub directory site and got the dedicated ip for my hosting account. The first time I probably did something wrong and screwed up my database so I asked my hosting provider to wipe everything and I started from the beginning again.
I carefully read the instruction and followed through. The result is that when I type in the domain name. Firefox says "Server not found. Firefox can't find the server at http://www.####.com."
But when I try to view a post, for example http://####.com/2012/02/26/hello-world/, it does work!