In reply to:
I have backups of most stuff, but do not have current backups of the ZenCart database for my online store, so I have a number of orders that I don't have access to.
Ouch! That's unfortunate indeed; *many* of us are guilty of being insufficiently diligent when i comes to backing up our databases (I wonder why that is the case?) 
In reply to:
And I frankly don't care what their logs say. I didn't do anything wrong, so shutting me down without warning was a mistake on their part.
It might be a mistake, but if you are not interested in "what their logs say" and just insist you did nothing wrong, well, that's fair enough, I suppose. That probably indicates there is little point in discussing it with them. Obviously, *something* happened; DH is not in the business of hosting websites to terminate customers accounts - they would rather continue to provide service and get paid for it. There are several things that I would not classify as "wrong" that are violations of TOS nonetheless - I suggest it might be more productive to try to discuss the situation with them and understand what caused them to suspend your account, but YMMV.
In reply to:
The fact that my ticket with support keeps getting deleted means they don't want to hear my side of the story at all.
As I, and others, have already pointed out, tech support is not likely to discuss this with you - rather the Abuse team will be handling it, and they are generally not as quick to respond as tech support (see an earlier post in this thread for a link to Jeff@dreamhost.com's comments on that).
Hey, you are in a rough situation and must be very frustrated. You can handle that frustration any way you choose; I just think you will be more productive and get better results if you take it up with the Abuse Team.
Complaining about it here may make you feel better, but is probably not as effective as handling it privately with DH.
--rlparker