Disk became full, had to force shutdown, now it doesn't boot
The problem is that the system goes into a fail-safe mode when the directory structure cannot be presumed to be safe for a new write.

You did the correct triage step by booting into recovery mode and attempting to repair the volume with Disk Utility.

At this point, you should back up any files you need. Test that your backup is complete and run Disk Utility against it to make sure it's in a good state.

Then you can boot to recovery and erase the volume or perhaps use another tool to repair the volume. If the drive erases and takes a format - the problem was a directory (data) corruption and not a hardware issue. If the disk can't be erased, then you need to repair the machine before restoring your backup onto a clean install of the OS.

In your case, you could possibly back up the changed files since 3 weeks or just get a new external drive and use Disk Utility to clone the volume or terminal to copy what you can using rsync or another tool.