I've been having the same Shut Down problem that you so graciously responded to above back in January 2016. As per your instructions I downloaded the Console file as you suggested and started looking back from the time the last entry prior to the Shut Down creating the blank screen with only the cursor present. The problem is I don't know how to interpret the prior system log entries. Any guidance would be greatly appreciated.
Thanks.
Jun 24 10:50:01 petersmac sessionlogoutd[422]: sessionlogoutd Launched
Jun 24 10:50:01 petersmac sessionlogoutd[422]: DEAD_PROCESS: 95 console
Jun 24 10:50:01 petersmac sharingd[252]: 10:50:01.055 : SCDynamicStoreCopyConsoleUser returned NULL
Jun 24 10:50:01 petersmac sharingd[252]: 10:50:01.055 : SDActivityAdvertiser::consoleUserChanged: Stopping for user 501 on logout
Jun 24 10:50:01 petersmac sharingd[252]: 10:50:01.055 : SCDynamicStoreCopyConsoleUser returned NULL
Jun 24 10:50:01 petersmac sharingd[252]: 10:50:01.056 : SCDynamicStoreCopyConsoleUser returned NULL
Jun 24 10:50:01 --- last message repeated 1 time ---
Jun 24 10:50:01 petersmac fseventsd[48]: implementation_removed_client: did not find client 0x7fa3f2202bc0 for path = '/.docid'
Jun 24 10:50:01 petersmac mdworker[391]: (ImportBailout.Error:1331) Asked to exit for Diskarb
Jun 24 10:50:01 petersmac mdworker[396]: (ImportBailout.Error:1331) Asked to exit for Diskarb
Jun 24 10:50:01 petersmac mdworker[394]: (ImportBailout.Error:1331) Asked to exit for Diskarb
Jun 24 10:50:01 petersmac mdworker[393]: (ImportBailout.Error:1331) Asked to exit for Diskarb
Jun 24 10:50:01 petersmac mdworker[413]: (ImportBailout.Error:1331) Asked to exit for Diskarb
Jun 24 10:50:01 petersmac mdworker[395]: (ImportBailout.Error:1331) Asked to exit for Diskarb
Jun 24 10:50:01 petersmac mdworker[414]: (ImportBailout.Error:1331) Asked to exit for Diskarb
Jun 24 10:50:01 petersmac com.apple.kextd[47]: Warning: /Volumes/Mac HD/System/Library/Extensions: No such file or directory
Jun 24 10:50:01 --- last message repeated 1 time ---
Jun 24 10:50:01 petersmac com.apple.kextd[47]: '/Volumes/Mac HD' updating, delaying reboot.
Jun 24 10:50:01 petersmac com.apple.kextcache[428]: Warning: /Volumes/Mac HD/System/Library/Extensions: No such file or directory
Jun 24 10:50:01 petersmac com.apple.kextcache[428]: rebuilding /Volumes/Mac HD/System/Library/Extensions.mkext
Jun 24 10:50:01 petersmac kernel[0]: hfs: unmount initiated on Mac HD on device disk3s2
Jun 24 10:50:01 petersmac com.apple.kextcache[428]: failed to create cache folder /Volumes/Mac HD/System/Library.
Jun 24 10:50:01 petersmac com.apple.kextcache[428]: Data error before mkext rebuild.
Jun 24 10:50:01 petersmac com.apple.kextcache[428]: Error 107 rebuilding /System/Library/Extensions.mkext
Jun 24 10:50:01 petersmac com.apple.kextcache[427]: /Volumes/Mac HD: no /usr/standalone/bootcaches.plist; skipping
Jun 24 10:50:01 petersmac com.apple.kextd[47]: helper error while updating /Volumes/Mac HD (error count: 1)
Jun 24 10:50:01 petersmac com.apple.kextd[47]: Warning: /Volumes/Mac HD/System/Library/Extensions: No such file or directory
Jun 24 10:50:01 petersmac com.apple.kextd[47]: / is still busy, delaying reboot.
Jun 24 10:50:01 petersmac com.apple.kextd[47]: Warning: /Volumes/Mac HD/System/Library/Extensions: No such file or directory
Jun 24 10:50:01 petersmac com.apple.kextd[47]: /Volumes/Mac HD is still busy, delaying reboot.
Jun 24 10:50:01 petersmac com.apple.kextd[47]: async child pid 428 exited with status 71
Jun 24 10:50:01 petersmac com.apple.kextcache[431]: /Volumes/Mac HD - No such file or directory.
Jun 24 10:50:01 petersmac com.apple.kextcache[432]: /Volumes/Mac HD - No such file or directory.
Jun 24 10:50:01 petersmac com.apple.kextd[47]: async child pid 431 exited with status 66
Jun 24 10:50:01 petersmac com.apple.kextd[47]: async child pid 432 exited with status 66
Jun 24 10:50:33 localhost bootlog[0]: BOOT_TIME 1466779833 0
The computer is an iMac late 2012 vintage with iCore 7 chipset running at 3.4 GHZ. 16 MB RAM and an external firewire HD (Mac HD) running off one of the Thunderbolt ports via an Apple Firewater Adapter. Most of the time the Shut down menu option will not work, but on 1 or 2 rare occasions it will.