The dates in the SQL Server error log look very strange. A subset for messages between Sep/29/2014 8:00 am and Sep/29/5:40pm show a date of Feb/16/2014. Have you seen this before? Any idea why the date would look different?
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Given that at 2/16/2014 12:23:46 AM the error message states that the instance has been using a process ID since 9/19/2014, I would suspect the system clock was rolled back after the instance startup. If this would be true we would also expect SSPI handshakes to fail due to clock difference between parties, and sure enough there are SSPI failures logged while the clock was adrift.