?
Current version of El Capitan, which is at version 10.11.3 (not 10.11.13 - check it!)
You may need to double-check that the OS X Server app has been updated, too, which would be version 5.0.15
And, as you would keep a current backup (it's a server system, correct), you could simply reinstall the last backup, and continue on as you were prior to the update.
If this was just a point update from 10.11.2 to 10.11.3, then it may be worthwhile to download current OS X full install from the App Store, then reinstall OS X.
You may also want to recheck the remote settings, as an OS X update MIGHT reset those to default.
Finally, before reinstalling, or restoring from a backup, you could look in the Actvity Monitor, which might point out what is causing the unresponsive system. Might be the you just need to reset the spotlight database file.