1)How did you setup the second domain? if it is pointed to a different shared account on the same server, then it should not be the problem…. how did you exactly asign the domain, did you only changed nameservers? or did you park it or some thing in the hosting account as well?
2)The problem seems to be with the installation itself, i say deleate it, and make the installation again, and make sure all the permissions are set up correctly….