Unfortunately, project.c3proj is the most important file.
You can try to create a blank project, then add all layouts, layers, event sheets, objects, behaviors, effects - with the same names as in your old project. (look up names in the unaffected folders).
After that save the new project as a folder, get the project.c3proj from it and and try injecting it into your old project.
This may be a difficult task and I am not sure if this will work. Don't forget to make backup copies of everything on every step!