To address your concerns with what OVH will and won't do:
OVH provide the dedicated servers unmanaged and as such they won't address software issues such as software on the server not starting up. This is easily verified by seeing if the server boots into rescue mode: once it does, the hardware is pretty much a.ok (although this is no guarantee) OR by reinstalling: a fresh install should be a known "good" state.
If it fails to boot while not in the rescue mode or not after a fresh install then it's a software problem -- outside the scope of what OVH can offer. This is normal for unmanaged servers, it takes a lot of (expensive) knowledge and know-how to be able to diagnose and fix every problem a customer can throw at them in a reasonable time. Such services will be quite expensive (I believe Rackspace offer this sort of thing).
This is a good thing: it keeps the costs of the servers down. OVH are one of the cheapest hosts around so it's an important aspect.
Another part of keeping costs down are limiting the services that OVH will (physically) perform on a server, catering a USB move would almost certainly increase the costs of USB drives (as well as still placing a limit on the number of moves -- so it would still not be that great). Moving a USB drive takes time and they probably do not want the (costly) hassle of moving the disk: if they make an exception to you, then they'll have to be able to do it for everyone.
While you're clearly frustrated, your attitude probably does not help the situation (why would they make an exception after being called a monkey?).
As for a solution, I see a couple of options (probably best in this order):
1) Boot into rescue mode, move everything of value to your USB drive and reinstall the server (it should leave the USB drive alone but make sure to select "install to first drive only"). You'll get a fresh boot of the OS, it will start up and you can recover from the USB drive.
2) Boot into rescue mode, mount the USB drive, then on your other server rsync the data to your new one. If it's another OVH server then it will not count against your bandwidth quota as it's internal traffic. It will probably
be faster than the time it takes for OVH to respond and move the disk themselves.
3) Ask for a quotation on a fix. I've never done this so I don't really know the steps but this is in the realm of "managed services", the
VIP page suggests you can ask for a quotation for £20, depending on their diagnosis you might have enough information to fix it yourself or just want them to get it over with and correct the issue.
Hope this helps! You should also consider setting up your system so that you can recover from any failure (back ups...), especially if it has something substantial behind it.