When I signed up with DreamHost a while ago, my account was approved and ready to go within 10-15 minutes. My domain was registered and fully propagated by early the next day.
Having said that; DreamHost do have an automated fraud detection system that can flag an application for manual approval. When this occurs, the delay for approval can stretch out to a few days. More information on this fraud detection system can be found at the URL below;
Of-course, just because your particular application triggers the fraud detection system, does not mean DreamHost thinks you are out to defraud them, it just means that the automated system has detected something within your application that it 'thinks' needs a closer look.
Also, the number of forum posts recently regarding promo-codes not working correctly, would seem to indicate that there may be a problem somewhere in the promo-code / referral system.
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