My Mac suffered a physical failure at the very beginning of the upgrade from El Capitan to Sierra. The physical failure has been fixed. I can get to the screen with Disk Utility, Reinstall OS and Time Machine options. But I don't have a Time Machine backup.
One option is to reinstall the OS. Would that wipe out my data? If so, what options are there for recovery?
The most important data are saved in a version control system, but there is always this and that around the edges that one would still want.