1: Avast is causing issues.
Code:
fffff880`0a1f5818 fffff880`03e2b7fbUnable to load image \SystemRoot\system32\drivers\aswSnx.sys, Win32 error 0n2
*** WARNING: Unable to verify timestamp for aswSnx.sys
*** ERROR: Module load completed but symbols could not be loaded for aswSnx.sys
aswSnx+0xe7fb
Uninstall Avast and Install MS Security Essentials and MalwareBytes.
Note
Make sure you uncheck the 'Enable Free Trial' box when installing.

2: Your ATI driver is old and needs updating.
Code:
0: kd> lmvm atikmdag
start end module name
fffff880`0482b000 fffff880`05341000 atikmdag T (no symbols)
Loaded symbol image file: atikmdag.sys
Image path: \SystemRoot\system32\DRIVERS\atikmdag.sys
Image name: atikmdag.sys
Timestamp: Wed Dec 19 20:38:55 2012 (50D225DF)
CheckSum: 00AC6529
ImageSize: 00B16000
Translations: 0000.04b0 0000.04e4 0409.04b0 0409.04e4
Download the 13.9 driver from here then use AMD Uninstall Utility to remove all traces of your current driver, CCC etc. Reboot and install the 13.9 driver.
Note
When installing choose 'Advanced' or 'Custom' (whichever option is available, just not Express) and uncheck everything except the video driver.
3: You've also received a few 0x124s which denote a hardware issue, but none of them are giving anything away as to what the issue actually is. Some of your other STOPs are pointing towards possible memory corruption though, so before we go into the full catalogue of hardware checks to stress your system follow the tutorial below to test your RAM first.
Code:
1: kd> !analyze -v
*******************************************************************************
* *
* Bugcheck Analysis *
* *
*******************************************************************************
WHEA_UNCORRECTABLE_ERROR (124)
A fatal hardware error has occurred. Parameter 1 identifies the type of error
source that reported the error. Parameter 2 holds the address of the
WHEA_ERROR_RECORD structure that describes the error conditon.
Arguments:
Arg1: 0000000000000000, Machine Check Exception
Arg2: fffffa8007aab028, Address of the WHEA_ERROR_RECORD structure.
Arg3: 00000000b60e4000, High order 32-bits of the MCi_STATUS value.
Arg4: 0000000000000135, Low order 32-bits of the MCi_STATUS value.
Download and run MemTest86+ to test your RAM.
Note
Run MemTest86+ for at least 8 passes. Ideally set it off before you go to bed and leave it overnight, we're looking for zero errors here. A single error will show something's going bad with your RAM.
It's possible your BIOS may be causing issues as it's quite old and may need updating, however we'll leave that until very last as flashing your BIOS does carry a substantial amount of risk which could lead to you turning your PC into a potato.
Did you actually update your BIOS in between some of these dumps occurring?
Code:
1: kd> !sysinfo machineid
Machine ID Information [From Smbios 2.5, DMIVersion 0, Size=2420]
BiosMajorRelease = 8
BiosMinorRelease = 15
BiosVendor = American Megatrends Inc.
BiosVersion = 0211
BiosReleaseDate = 07/08/2009
Code:
1: kd> !sysinfo machineid
Machine ID Information [From Smbios 2.5, DMIVersion 0, Size=2420]
BiosMajorRelease = 8
BiosMinorRelease = 15
BiosVendor = American Megatrends Inc.
BiosVersion = 2105
BiosReleaseDate = 07/23/2010