You're talking in circles. Unless you have a port number on the URL, you have to deal with port 80, http's well known port number.
If you're using a URL of 192.168.1.34/~username/ you must have /Users/username/Sites/index.html in place. If the file is named anything else, the default configuration of Apache won't look for it. Depending on how Apache's configged, it could give a 403 Permission denied error for other reasons.
One thing, Apache uses the *nix on OSX, and is case sensitive, that may be getting you.
Could you look at /var/log/httpd/error_log and post a couple of the messages? That would be very helpful in troubleshooting this.
Roger