This one was purely coincidental, and not really anything to do with us (the VA). Something we had disabled more than 6 months ago randomly turned itself back on and swallowed up all the free disk space on the server, which quite understandably got upset and refused to do anything as a result. Our hosting provider is looking into why said disabled thing chose to randomly re-enable itself, and with a bit of luck this particular problem won't re-occur.
Management would like to thank EHM-2589 David Sifuentes for bringing this to our attention (and I'd like to thank E-J/Dom for forwarding it onto me since I don't have a Facebook account any more

)