Dir open: Could not open directory 'slots/0' from '/var/lib/boinc-client'

Simply said, you have a permission problem when you get an error like this.
To fix this, you can either:

• reinstall BOINC;
  
• check that you're using the correct user to run BOINC.
  
• slow down BOINC start at OS start-up, to allow all drivers to load first, see man sleep.