Mac mini hung with multiple gpuRestart files logged, what to do?

Question

My Mac mini (Late-2012) decided to freeze during the night. Now in the morning I was greeted with the plain boot-screen (Apple logo and progress bar) that was hung at about 50%. After waiting 30 min I manually rebooted the system. It came back on but was initially super-sluggish, took me 5 minutes to get to the desktop.
Checking the system messages I saw about 20 logs with the name Kernel_2015-03-15-012435_NANNA.gpuRestart (timestamp varying 30 secs). I won't bore you with the full details, but the start of the file is listed below.
My system hooks up to a Samsung monitor using DP and has never acted up like this before.
The 10.10.2 update was made as soon as it was released.
Power Nap is disabled, I normally leave the system on and let the computer sleep function kick in after 45 minutes.
What should I do?
/Mattias
Sun Mar 15 01:24:36 2015
Event:               GPU Reset
Data/Time:           Sun Mar 15 01:24:36 2015
Application:        
Path:               
OS Version:          Mac OS X Version 10.10.2 (Build 14C1510)
Graphics Hardware:   Intel HD Graphics 4000
Signature:           801
Report Data:
===========================================================================
                         Intel GPU Hang Summary
                              version 1.0.0
===========================================================================
-- Summary of Status for ALL Rings --
MAIN Ring is idle
MEDIA Ring is NOT enabled
BLT Ring is NOT enabled
===========================================================================
                     Essential Ring Registers
===========================================================================
-- MAIN Ring --
  RING_HEAD   = 0x00000048  (offset = 0x00000048, wrap count = 0, wait_for_cond = 0x0)
  RING_TAIL   = 0x00000048  (offset = 0x00000048)
  RING_START  = 0x10204000  (offset = 0x10204000)
  RING_CTRL   = 0x0000f001  (enabled, auto report disabled (0x00), not waiting, semaphore not waiting, length = 0x010 4KB pages)
-- MEDIA Ring --
  RING_HEAD   = 0x00000000  (offset = 0x00000000, wrap count = 0, wait_for_cond = 0x0)
  RING_TAIL   = 0x00000000  (offset = 0x00000000)
  RING_START  = 0x00000000  (offset = 0x00000000)
  RING_CTRL   = 0x00000000  (disabled, auto report disabled (0x00), not waiting, semaphore not waiting, length = 0x001 4KB pages)
-- BLT Ring --
  RING_HEAD   = 0x00000000  (offset = 0x00000000, wrap count = 0, wait_for_cond = 0x0)
  RING_TAIL   = 0x00000000  (offset = 0x00000000)
  RING_START  = 0x00000000  (offset = 0x00000000)
  RING_CTRL   = 0x00000000  (disabled, auto report disabled (0x00), not waiting, semaphore not waiting, length = 0x001 4KB pages)
- Common Slice INST_DONE register -
  All Common Slice engines are done.
   - INSTDONE_CS (=0xffffffff): Not done =
===========================================================================
                          MMIO Register Dump
===========================================================================

Answer 1

The logic board is failing, or there is some other internal hardware fault. The hardware test is unreliable.
Make a "Genius" appointment at an Apple Store, or go to another authorized service provider. You may have to leave the machine there for several days.
Back up all data on the internal drive(s) before you hand over your computer to anyone. There are ways to back up a computer that isn't fully functional—ask if you need guidance.
If privacy is a concern, erase the data partition(s) with the option to write zeros* (do this only if you have at least two complete, independent backups, and you know how to restore to an empty drive from any of them.) Don’t erase the recovery partition, if present.
Keeping your confidential data secure during hardware repair
Apple also recommends that you deauthorize a device in the iTunes Store before having it serviced.
*An SSD doesn't need to be zeroed.