Hard to be sure from your post, but I'm thinking you can't boot Windows at all?
Any chance you have access to an installation disk for the OS? A "repair" install could be carried out, and that would likely at least make it boot-able, to at least recover your data, and maybe get a working unit again with possibly much less than 10 hours of work.
Once it is boot-able, the Avast chest will be accessible, and as many files as possible (FPS only, of course) should be restored.
I doubt a system restore would work, as even if the restore point was functioning (and there might be some that still function) without the actual files present, the restore would only bring back the registration of what was present. If that is now absent, (depending on which files were sent to the chest) all you'll get is more errors.
OS disk is the best bet.
The "disk is full" error would relate to the vault, not the hard drive. It has a default maximum size. (256Mb, IIRC.)
For the future, can I recommend an imaging program, something 3rd party that is capable of taking an image of your drive, for later restoration should things like this happen? I use Macrium reflect. Others use Acronis, Norton Go Back... there are a few.
Faulty software is one of many things that can render an OS unusable. A backup program helps reduce stress/time needed to fix.