BSOD at completely random times. Help would be appreciated.

You've got an issue with the ATI driver you most likely recently updated:

Code:

1: kd> .bugcheck
Bugcheck code 1000007E
Arguments ffffffff`c0000005 fffff880`11125160 fffff880`0911edd8 fffff880`0911e630

// The exception record indicates something tried to read from the memory address 0x0000000000000030, which is of course a big no-no:
1: kd> .exr fffff880`0911edd8
ExceptionAddress: fffff88011125160 (atikmdag!DrmDmaPktInterface::Copy)
   ExceptionCode: c0000005 (Access violation)
  ExceptionFlags: 00000000
NumberParameters: 2
   Parameter[0]: 0000000000000000
   Parameter[1]: 0000000000000030
Attempt to read from address 0000000000000030

// The stack clearly indicates that the ATI driver is attempting to write memory to that address for some reason:
1: kd> kn
 # Child-SP          RetAddr           Call Site
00 fffff880`0911f018 fffff880`1118e539 atikmdag!DrmDmaPktInterface::Copy
01 fffff880`0911f020 fffff880`1118cbb6 atikmdag!DrmDmaPagingContext::PagingWriteDeferredPtUpdateCmds+0x2c9
02 fffff880`0911f0d0 fffff880`1118f1a7 atikmdag!DrmDmaPagingContext::CommonPtUpdate+0x306
03 fffff880`0911f160 fffff880`1106c764 atikmdag!DrmDmaPagingContext::Transfer+0x257
04 fffff880`0911f1f0 fffff880`0743609e atikmdag!Dispatch_BuildPagingBuffer+0x434
05 fffff880`0911f370 fffff880`07436217 atikmpag!ProxyBuildPagingBuffer_WDDM1x+0x5fe
06 fffff880`0911f400 fffff880`122df9ac atikmpag!ProxyBuildPagingBuffer+0x23
07 fffff880`0911f430 fffff880`11022a28 dxgkrnl!DXGADAPTER_DdiBuildPagingBuffer+0x50
08 fffff880`0911f460 fffff880`110227db dxgmms1!VIDMM_GLOBAL::MemoryTransferInternal+0x198
09 fffff880`0911f5f0 fffff880`1102f2ad dxgmms1!VIDMM_GLOBAL::MemoryTransfer+0x193
0a fffff880`0911f690 fffff880`11021c2b dxgmms1!VIDMM_MEMORY_SEGMENT::CommitResource+0x1fd
0b fffff880`0911f770 fffff880`1101e887 dxgmms1!VIDMM_GLOBAL::PageInAllocations+0xbb
0c fffff880`0911f7d0 fffff880`110387d9 dxgmms1!VIDMM_GLOBAL::PrepareDmaBuffer+0xccf
0d fffff880`0911f9a0 fffff880`11038514 dxgmms1!VidSchiSubmitRenderCommand+0x241
0e fffff880`0911fb90 fffff880`11038012 dxgmms1!VidSchiSubmitQueueCommand+0x50
0f fffff880`0911fbc0 fffff800`0356273a dxgmms1!VidSchiWorkerThread+0xd6
10 fffff880`0911fc00 fffff800`032b78e6 nt!PspSystemThreadStartup+0x5a
11 fffff880`0911fc40 00000000`00000000 nt!KxStartSystemThread+0x16
 
// Context record showing the attempt to copy to an invalid/inaccessible address:
1: kd> .cxr 0xfffff8800911e630
rax=0000000000000000 rbx=0000000000000000 rcx=0000000000000000
rdx=0000000000000000 rsi=fffffa80078a09f8 rdi=0000000000000001
rip=fffff88011125160 rsp=fffff8800911f018 rbp=fffffa80078a09f8
 r8=0000000000050000  r9=0000000000000000 r10=fffff880112a2390
r11=fffff88006ff0164 r12=fffffa8007906010 r13=0000000000000000
r14=0000000000000001 r15=fffffa800a86ddf8
iopl=0         nv up ei ng nz na pe nc
cs=0010  ss=0018  ds=002b  es=002b  fs=0053  gs=002b             efl=00210282
atikmdag!DrmDmaPktInterface::Copy:
fffff880`11125160 488b4130        mov     rax,qword ptr [rcx+30h] ds:002b:00000000`00000030=????????????????


// The driver seems quite new................
1: kd> lmDvm atikmdag
start             end                 module name
fffff880`11058000 fffff880`122dc000   atikmdag   (pdb symbols)          C:\debuggers\sym\atikmdag.pdb\3A4DCFB371244B659CB90810F1B45C411\atikmdag.pdb
    Loaded symbol image file: atikmdag.sys
    Mapped memory image file: C:\debuggers\sym\atikmdag.sys\546EA3C31284000\atikmdag.sys
    Image path: \SystemRoot\system32\DRIVERS\atikmdag.sys
    Image name: atikmdag.sys
    Timestamp:        Thu Nov 20 18:30:27 2014 (546EA3C3)
    CheckSum:         0121F198
    ImageSize:        01284000
    File version:     8.1.1.1443
    Product version:  8.1.1.1443
    File flags:       8 (Mask 3F) Private
    File OS:          40004 NT Win32
    File type:        3.4 Driver
    File date:        00000000.00000000
    Translations:     0409.04b0
    CompanyName:      Advanced Micro Devices, Inc.
    ProductName:      ATI Radeon Family
    InternalName:     atikmdag.sys
    OriginalFilename: atikmdag.sys
    ProductVersion:   8.01.01.1443
    FileVersion:      8.01.01.1443
    FileDescription:  ATI Radeon Kernel Mode Driver
    LegalCopyright:   Copyright (C) 1998-2012 Advanced Micro Devices, Inc.

You should probably roll back to a previous known-good driver version, or, short of that, start up a thread with ATI support if that isn't possible or doesn't work.