Multisite on a new server

Newbie here.

I am currently using Drupal 6.22 on a shared server. The hosting company decided to move to new hardware and the move has been a disaster for the users and tech support.

I have a multisite installation that is currently working on their old servers at a4skyhawk.org and how long they will be able to point to that server is a question nobody can answer. With the move to the new server there has been some corruption in unknown files on my installation and I am trying to figure out the problems.

My question is this:

How do I access a site other than the default installation when using 123.45.567.89/~abcde since I do not yet have the domain pointed to the new hardware?

What occurs when I use 123.45.567.89/~abcde is that the drupal install page comes up, I then enter in the database information, the system notices that I already have a site installed and allows me to select the previously installed site. However, in the process, the sites/default settings.php becomes modified with that database information and becomes the primary install. Since there are no modules or files installed in the sites/default folder, I am stuck with a broken installation (until I reset the settings.php) since I have all of my files in the sites/a4skyhawk.org directory. When I visit 123.45.567.89/~abcde/user, I receive a 404 Not Found (port 80) error.

I've visited multiple pages that address the multisite installation problems and modifying the .htaccess Rewrite Base and settings.php base url have had no effect. Currently, I have installed the site directly into the public_html directory and not in public_html/drupal in order to hopefully figure this out. My plan is to reinstall in a /drupal subdirectory at a location that will be easier to upgrade.

Thanks in advance.