You need to use the support form https://www.dreamhost.com/support/ to contact support.
It gets tricky tho if the broken email is the only email address you have on your account. Dreamhost protects customers privacy to the point that they don’t answer queries like this when they think may be fraudulent. Send as much info as you can with your request to prove you are the correct person. First and last four digits of the credit/debit card attached to the account will go a long way. Considering dreamhosts size they probably get at least a couple daily fraudulent requests to get into an account. (Consider Ex-Employess wanting to harm the former employer, estranged spouses that want to be nosy, etc etc)
Queries like this will be handled by the normal 9-5 mon-fri staff… 24/7 tech support won’t answer these.
After you get back into your account be sure to add gmail/yahoo/etc email to your account. And fill out the password/account recovery security questions. I would also switch from the IP based authentication to multi-factor authentication which is much more convenient for a couple of reasons.