there should be no reason that Mail.app or Thunderbird or even webmail shouldn't be able to display that many messages. Sure, it taxes the server a bit more than if you only had 1GB of email or whatever. But if the data is there, it should just work.
That the email doesn't show up in your webmail in the old-messages folder indicates to me that they aren't actually in that location.
Some webmail clients, in the settings for webmail, have a place where you can "subscribe" to various folders within the email account. In this way, there might be folders with email that are stored on the server, but that aren't showing up in your webmail client for some reason. See if you have an option like that. Mail.app or other similar programs should download/display all email folders within your account, regardless of the "subscribed" folder settings in webmail (in most cases). If you are not seeing the messages in Mail.app, I'm a little more suspicious that the mail may not actually be there.
The other place I'd look is to login to SFTP to see if you can find any evidence of your email there. I'm not familiar with how Dreamhost email is setup, but on many hosts, there will be an email folder one level above the "public_html" directory that has all your email stored there. Those files are where your email is stored, and you may want to check to see if anything is there.
One other thing I might try --
Look in your Dreamhost mail control panel (like where you would setup a new email address). See what size the account is reported as using. If it's the 33gb size, that's fine. Then, in Mail.app, right-click on the inbox for the account in question. Select "Account info" and let Mail calculate all the mailbox sizes. How does that total number compare with the total that Dreamhost reports?
You can also see in that "account info" window a "subscription list". Just look in there to make sure there aren't any directories that are presently unsubscribed.
There are a few other things you might try, but start with some of these and see what you get.