Thanks for the info Damiano!
I too researched the "Illegal group reference" error, but no luck matching it to any existing ArcGIS/ESRI issues. The closest thing I get is errors with the $ character in java.
That being said, the most probable issue here, in my opinion, is that the server restart caused some form of issue or corruption of the data store/config store or the directory links.
My first step would be to go into the ArcGIS for Server Manager, and try to modify the directories links and see if it might recreate a corrected path for the server. If that doesn't work, is there a recent backup of the physical location of the data store/config store/directories list and can you retrieve a known good copy from there? Other than these options, I can't think of anything else that might restore your services.