Hi Sarevok9,

I have analyzed your dump files and the latest dump file blames the Direct X package file "dxgmms1.sys". Below has been provided a summary of that :-
Code:
**************************Tue Jul 22 07:31:49.412 2014 (UTC + 5:30)**************************
Probably caused by : dxgmms1.sys ( dxgmms1!VidMmProcessAsyncOperation+1a )
 
BugCheck 139, {3, ffffd00021a966d0, ffffd00021a96628, 0}
BugCheck Info: KERNEL_SECURITY_CHECK_FAILURE (139)
 
BUGCHECK_STR:  0x139
 
DEFAULT_BUCKET_ID:  LIST_ENTRY_CORRUPT
 
PROCESS_NAME:  System
 
FAILURE_BUCKET_ID:  0x139_3_dxgmms1!VidMmProcessAsyncOperation
 
MaxSpeed:     3500
 
CurrentSpeed: 3500
 
  BIOS Version                  1402
 
  BIOS Release Date             03/21/2014
 
  Manufacturer                  System manufacturer
 
  Product Name                  System Product Name
 
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Below is a list of 3rd party drivers found on your system :-
Code:
**************************Tue Jul 22 07:31:49.412 2014 (UTC + 5:30)**************************
nm3.sys                     Thu Jun 10 05:35:51 2010 (4C102C5F)
HECIx64.sys                 Tue Jul  3 03:44:58 2012 (4FF21D62)
lvrs64.sys                  Tue Oct 23 07:41:24 2012 (5085FCCC)
lvuvc64.sys                 Tue Oct 23 07:42:08 2012 (5085FCF8)
Rt630x64.sys                Fri May 10 15:29:08 2013 (518CC4EC)
intelppm.sys                Thu Aug 22 14:16:35 2013 (5215CFEB)
dump_storahci.sys           Thu Aug 22 17:10:39 2013 (5215F8B7)
nvhda64v.sys                Thu Nov 28 19:08:09 2013 (52974741)
BootDefragDriver.sys        Mon Mar  3 14:03:27 2014 (53143E57)
nvvad64v.sys                Fri Mar 28 19:02:06 2014 (533579D6)
NvStreamKms.sys             Thu May 22 22:13:14 2014 (537E2922)
nvlddmkm.sys                Fri Jun 13 05:48:13 2014 (539A4345)
GUBootStartup.sys           Mon Jun 23 08:26:24 2014 (53A79758)
http://www.carrona.org/drivers/driver.php?id=nm3.sys
http://www.carrona.org/drivers/driver.php?id=HECIx64.sys
http://www.carrona.org/drivers/driver.php?id=lvrs64.sys
http://www.carrona.org/drivers/driver.php?id=lvuvc64.sys
http://www.carrona.org/drivers/driver.php?id=Rt630x64.sys
http://www.carrona.org/drivers/driver.php?id=intelppm.sys
http://www.carrona.org/drivers/driver.php?id=dump_storahci.sys
http://www.carrona.org/drivers/driver.php?id=nvhda64v.sys
http://www.carrona.org/drivers/driver.php?id=BootDefragDriver.sys
http://www.carrona.org/drivers/driver.php?id=nvvad64v.sys
http://www.carrona.org/drivers/driver.php?id=NvStreamKms.sys
http://www.carrona.org/drivers/driver.php?id=nvlddmkm.sys
http://www.carrona.org/drivers/driver.php?id=GUBootStartup.sys

Make sure the highlighted drivers are updated. This is to ensure that these are not causing any problems. Most of the dump files blame the Direct X.

Furthermore, according to my search, it seems that the GTX 780 requires a MINIMUM (Note that, since your system is automatically overclocking itself, you would need a bit more) of 600W PSU for proper functioning whereas the AMD R9-270 requires a PSU of 500 W.

I would ask you to run the GPU Stress test using this **GUIDE** and see if it is crashing or producing some weird artifacts or not(NVIDIA one).
One thing which must be made sure is that the system is running stable while the AMD R9-270 is plugged in. Let me know the results ^_^.