There are a couple of ways to find out what server you are on.
The easiest way is via the panel. Go to Users -> Manage Users, the server name is shown under the Machine column for the user that controls that domain.
The second way is to log-in via SSH, the server name is shown using large ASCII characters.
Of-course, the answer to this depends on exactly what you mean by your site being ‘down’. If the domain transfer went smoothly and your site was previously working on DreamHost (even for a day or so) then the issue you are experiencing is unlikely to be due to the domain transfer.
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