I'm having the same problem since upgrading to El Capitan. If I reboot, shutdown, or logoff from the Apple menu, all programs close and the menu bar and desktop icons disappear, but the dock stays. Finder says Application not responding, and it doesn't relaunch. I can open other apps, however. I've been shutting down via command line in Terminal, which works but also seems a bit slower than I expect.
I thought I had a breakthrough after running DiskWarrior 5 and repairing, and a successful reboot... but it was a one-off. It's back to how it was again.
I've tried trashing my com.apple.finder.plist without luck. I've repaired via Disk Utility both in OS and Recovery, and with Disk Warrior. I've shut down all other programs and many background processes before trying to reboot.
It very consistently does the same thing every time. Any ideas or more things to try?