You have been given some good information here by the other responders, but I think you might be missing the point in a couple of ways.
That kind of qualification doesn't make a log of sense to me ...if it is subject to copyright protection and you do not have the right to make a copy of it, irrespective of where you ultimately store it, or whether you make it available to others, it is "illegally copied" - I don't get the "somewhat" part. Sure, we are getting near "holy war" territory here, and there are many who argue the "law" is not "right", but the way the law sits now in the United states (and most other Berne Convention signatories) a "copy" that you do not have the legal right to make is "illegal"
What are you asking? Does the Windows9SE EULA allow you to copy and "backup" or archive it? What are your legal "rights" in "backing up" those songs? It seems that you are asking if it is "OK" to store your own "illegally copied" files on DH's server as long as you don't distribute them. Note from the Abuse Center that Lensman linked you to:
For the purposes of our policies, 'storage' involves the storage of copyrighted material that was obtained unlawfully. So, if you use BitTorrent or some other tool from your own computer to illegally obtain a DVD rip and then store a copy under your DreamHost account (even if it's not being re-distributed), such activity would be prohibited."
Actually, I think that first sentence is pretty clear, and the second sentence lists one example of prohibited activity that is essentially the same as what you are proposing.
Reading the first sentence above literally, the second sentence might also be written (or an additional clarification of that first sentence might read):
"So, if you illegally create a copy of a song, or a software program, and then store a copy under your DreamHost account (even if it's not being re-distributed), such activity would be prohibited."
You might also ask yourself how the kind of "storage" or "backup" usage you are describing relates to the TOS section regarding "Lawful Purpose":
- Customer may only use DreamHost Web Hosting's Server for lawful purpose. Transmission of any material in violation of any Country, Federal, State or Local regulation is prohibited. To this effect, child pornography is strictly prohibited as well as housing any copyrighted information (to which the customer does not hold the copyright) on DreamHost Web Hosting's Server."
I'd take special note of the words "transmission" and "housing", and note that that neither of those terms imply "distribution", though they do imply "uploading to or from" and "storing".
It seems to me that the sections of the TOS and the Abuse Center documentation make it pretty clear that doing what you describe is prohibited.
Now, I may be completely wrong on all of this - and some of the other answers you have received here may also be wrong. I strongly suggest ,if you really want the authoritative answer, you write firstname.lastname@example.org with your question and see what they say. If they do not intend to allow such "storage", I think it is better to know that now than to find yourself protesting, "But, they told me in the forum it was probably OK!", when/if you find your account suspended or terminated.
If it were me, I wouldn't chance it - I can't see any advantage to me to use the storage that way; it's easy enough to burn a backup DVD or CD, and that meets my purposes just fine.
Again, why trust anything you read here? Just write DreamHost and ask them straight-out.