My brand new system is randomly freezing and I don't know how to debug the issue.

System:

• AMD A10-5800k
• Asus F2A85-M motherboard
• Integrated Radeon HD 7660D
• 8gb Samsung ddr3 1600
• Ubuntu 12.10
• Gnome shell / Unity (issue exists in both)

xorg.conf (relevant parts):

Section "Device"
    Identifier  "aticonfig-Device[0]-0"
    Driver      "fglrx"
    BusID       "PCI:0:1:0"
    Option      "TexturedVideoSync" "on"
    Option      "UseFastTLS" "2"
EndSection

Section "Screen"
    Identifier "aticonfig-Screen[0]-0"
    Device     "aticonfig-Device[0]-0"
    Monitor    "Monitor0"
    DefaultDepth     24
    Option      "UseEDID" "False"
    Option      "ExactModeTimingsDVI" "True"
    Option      "NoBandWidthTest" "true"
    Option      "ModeValidation" "AllowNon60hzmodesDFPModes, NoEDIDDFPMaxSizeCheck, NoVertRefreshCheck, NoHorizSyncCheck, NoDFPNativeResolutionCheck, NoMaxSizeCheck, NoMaxPClkCheck, NoEDIDModes"
    Option      "UseEDIDDPI" "False"
    Option      "UseEDIDFreqs" "0"
    Option      "NoLogo" "True"
    Option      "Coolbits" "1"
    Option      "metamodes" "DFP-0: 2560x1440_60 +0+0"
    SubSection "Display"
        Depth     24
        Modes    "2560x1440"
    EndSubSection

• I ran memtest on my ram and it checks out fine.
• I have tried using the latest fglrx and fglrx-beta.
• I have loaded 3.6.x kernel.
• I do not see anything relevant in dmesg, kern.log, syslog, .xsession-errors or Xorg.log.
• I cannot ssh into the machine when frozen from another machine.
• I know that system resources not being stressed when the crashes happen.
• It seems that video and any gaming (very simple graphics games) contribute to the freezes most frequently. However, I have experienced the crash before when just using Chrome.
• I suspect the crashes are xorg/fglrx related, but I have no evidence to back that up.

Where should I look? What should I grep for? What should I try next?