Boot drive failed; external backup drive not being seen

Question

I've had a Windows Server 2012 Essentials machine (6 drives + 1 external USB 3TB dedicated backup) running fine for over a year now.  The system backup was configured through the Essentials Dashboard, the backup drive was found automatically by
Windows without any custom drivers, and was successfully backing up as scheduled.  A few days ago, the server rebooted for an update, and started blue-screening early on during the boot.  Using the install media, I went to the restore facility, but
the dedicated external USB backup drive isn't being found (the restore list is empty).  I tried using other USB ports (they all work, as tested with the keyboard), but the backups on it still aren't showing.  Moving the backup drive to a nearby Windows
8.1 machine, it shows up correctly in the Disk Manager (the name is correct; no drive letter assigned, as expected).  From the system-recovery command-line on the server, wbadmin get drives show it, but as [not mounted].
What should my next steps be?  Is it safe to mount it to a drive letter on the Windows 8.1 machine and share it out, or will that irreparably damage the backups?  Is there something obvious I'm missing?  Why isn't the Windows Server 2012 Essentials
install media's repair functionality finding it (this should be a no-brainer, right?)?
The drive in question is a Seagate model SRD00F2.
Thanks!

Answer 1

1. What updates has been installed. See info in WindowsUpdate.log.
2. Hope you has not installed optional drivers. It this is true try to return back or reinstall drivers from server vendor support page (perhaps support for USB 3)
3. What do Event lods and Device Manager say?
Rgds
Milos
The reboot was overnight (about 4am) on Sunday, 2014-04-13.  It was for the latest updates from Microsoft at that time (so the prior Tuesday's batch; see below for the details from WindowsUpdate.log).
No optional drivers installed, other than the motherboard ones at initial system load.  They've been running great for a year or so now.  They weren't part of the update.
Not possible to check.  Trying to boot into safe mode also blue screens fairly early on during boot (about 15-20 seconds; same error).  Boot logging never generates a log because it doesn't get far enough to dump to disk.
From WindowsUpdate.log:
Updates to install = 2
2014-04-13 03:06:45:513 492 f30 Agent  *   Title = Cumulative Update for Internet Explorer 10 for Windows Server 2012 (KB2936068)
2014-04-13 03:06:45:513 492 f30 Agent  *   UpdateId = {783D8F98-1563-4735-B1A3-3E3BB2D86532}.200
2014-04-13 03:06:45:513 492 f30 Agent  *     Bundles 1 updates:
2014-04-13 03:06:45:513 492 f30 Agent  *       {1BBB8E66-7F5E-4CA2-9EB2-80117D4D84D9}.200
2014-04-13 03:06:45:513 492 f30 Agent  *   Title = Update for Windows Server 2012 (KB2928678)
2014-04-13 03:06:45:513 492 f30 Agent  *   UpdateId = {8F7E4DBD-BE3F-463B-BB5A-55B33039A023}.201
2014-04-13 03:06:45:513 492 f30 Agent  *     Bundles 1 updates:
2014-04-13 03:06:45:513 492 f30 Agent  *       {8D7948A9-3FD9-4430-B790-0511A7CB4502}.201
2014-04-13 03:06:46:093 492 f30 Report ***********  Report: Initializing static reporting data  ***********
2014-04-13 03:06:46:093 492 f30 Report  * OS Version = 6.2.9200.0.0.131377
2014-04-13 03:06:46:093 492 f30 Report  * OS Product Type = 0x00000032
2014-04-13 03:06:46:109 492 f30 Report  * Computer Brand = System manufacturer
2014-04-13 03:06:46:109 492 f30 Report  * Computer Model = System Product Name
2014-04-13 03:06:46:109 492 f30 Report  * Platform Role = 1
2014-04-13 03:06:46:109 492 f30 Report  * AlwaysOn/AlwaysConnected (AOAC) = 0
2014-04-13 03:06:46:125 492 f30 Report  * Bios Revision = 0211
2014-04-13 03:06:46:125 492 f30 Report  * Bios Name = BIOS Date: 07/02/12 16:24:26 Ver: 04.06.05
2014-04-13 03:06:46:125 492 f30 Report  * Bios Release Date = 2012-07-02T00:00:00
2014-04-13 03:06:46:125 492 f30 Report  * Bios Sku Number = SKU
2014-04-13 03:06:46:125 492 f30 Report  * Bios Vendor = American Megatrends Inc.
2014-04-13 03:06:46:125 492 f30 Report  * Bios Family = To be filled by O.E.M.
2014-04-13 03:06:46:125 492 f30 Report  * Bios Major Release = 4
2014-04-13 03:06:46:125 492 f30 Report  * Bios Minor Release = 6
2014-04-13 03:06:46:125 492 f30 Report  * Locale ID = 1033
2014-04-13 03:06:46:702 492 f30 DnldMgr Adding revision ID 200 for update 1BBB8E66-7F5E-4CA2-9EB2-80117D4D84D9 to the lock revision cache.
2014-04-13 03:06:46:702 492 f30 DnldMgr Preparing update for install, updateId = {1BBB8E66-7F5E-4CA2-9EB2-80117D4D84D9}.200.
Other pieces of interest after that:
2014-04-13 03:20:12:900 8984 30e0 Handler FATAL: CBS called Error with 0x80071a30, 
 ...and...
2014-04-13 03:20:21:047
492 26dc
Report REPORT EVENT: {E979933C-EE46-4395-8C2C-8E09543CAABE}
2014-04-13 03:20:15:665-0700 1
195 [AU_SCHEDULED_INSTALL_FAILED] 101
{783D8F98-1563-4735-B1A3-3E3BB2D86532}
200 80071a30
AutomaticUpdates Failure
Content Install Installation Failure: Windows failed to install the following update with error 0x80071a30: Cumulative Update for Internet Explorer 10 for Windows Server 2012 (KB2936068).
2014-04-13 03:20:21:172
492 26dc
Report CWERReporter::HandleEvents - WER report upload completed with status 0x8
2014-04-13 03:20:21:172
492 26dc
Report WER Report sent: 7.8.9200.16731 0x80071a30(0x80071a30) 783D8F98-1563-4735-B1A3-3E3BB2D86532 Install 101 Unmanaged
2014-04-13 03:20:21:172
492 26dc
Report CWERReporter finishing event handling. (00000000)
2014-04-13 03:30:34:845
8984 1084
Handler Requesting post-reboot reporting for package Package_for_KB2928678~31bf3856ad364e35~amd64~~6.2.1.1.
2014-04-13 03:30:34:845
8984 1084
Handler Completed install of CBS update with type=3, requiresReboot=1, installerError=0, hr=0x0
 ...and...
2014-04-13 03:31:09:364
492 33a8
AU  # WARNING: Install call completed, reboot required = Yes, error = 0x00000000
 ...and...
2014-04-13 03:31:09:364
492 1f9c
AU Install complete for all calls, reboot  needed
2014-04-13 03:31:09:364
492 1f9c
AU CAUInstaller::OnAllCallsComplete |  result of install HRESULT hr = 0x80071A30
 ...and...
2014-04-13 03:41:11:933
492 1f9c
Misc WARNING: SUS Client is rebooting system.
After that, there's just some shutting down client and such notices for the reboot.