Right there is the problem. Dreamhost simply can’t be in the business of passing information between customers, it’s not for them to decide whose property is whose. While you have painted an emotional picture where it’s a site for a “good cause” so this must be the right thing for dreamhost to do, on the other hand the previous site owner might have very purposely NOT given the content to the previous site, they may have made the choice, I don’t want to run it anymore and I’ll pass the name on, but choose not to pass the content. If dreamhost decided, “well we should just copy the site over–after all it is the same domain.” That might be expressly what the original site owner didn’t want. (Or perhaps the original owner offered the content for a price, and that was declined… there are many scenarios.)
Now after saying all that, there is still hope for you. Contact the original account owner and ask THEM for site backups and database backups. At the time they deleted hosting for the domain, so it could be added to a different dreamhost account, all that happaned was the DNS was removed and it was deleted from the apache config of the server. The files and databases for the site are NOT deleted by those actions. For the database and files for the site to get deleted someone would need to manually do that, or the entire dreamhost account would need to be cancelled. So as long as the account is still in good standing, and they didn’t expressly delete the content, it does still exist on the original server.
If the above fails, it may still be possible to reconstruct the site using archive.org, but that takes more time and skill.