BSOD While Gaming! (Star Trek Online)

OK, it looks like you've eliminated all the problem drivers. The 2 remaining 2009 drivers are actually the latest version available (ASACPI.sys and GearAspiWDM.sys). That means that, most likely, you've got a hardware problem.
Just to be sure, please run Driver Verifier according to these instructions: Driver Verifier Settings

Once you post the memory dumps from Driver Verifier, turn it off and start with these free hardware diagnostics: Hardware Diagnostics

The following info is just FYI, I've already addressed the issues that I saw in the above paragraphs

- Further info on BSOD error messages available at: http://www.carrona.org/bsodindx.html
- Info on how to troubleshoot BSOD's (DRAFT): http://www.carrona.org/userbsod.html
- How I do it: http://www.carrona.org/howidoit.html

3RD PARTY DRIVERS PRESENT IN THE DUMP FILES

Code:

ASACPI.sys      Wed May 13 21:25:17 2009 (4A0B72FD)
GEARAspiWDM.sys Mon May 18 08:17:04 2009 (4A1151C0)
MpFilter.sys    Fri Mar 09 06:05:26 2012 (4F59E3F6)
amdxata.sys     Fri Mar 19 12:18:18 2010 (4BA3A3CA)
nvhda64v.sys    Wed Apr 18 13:07:54 2012 (4F8EF4EA)
nvlddmkm.sys    Tue May 15 03:35:36 2012 (4FB20748)
rtl8192Ce.sys   Tue Jun 14 23:05:06 2011 (4DF82162)

http://www.carrona.org/drivers/driver.php?id=ASACPI.sys
http://www.carrona.org/drivers/driver.php?id=GEARAspiWDM.sys
http://www.carrona.org/drivers/driver.php?id=MpFilter.sys
http://www.carrona.org/drivers/driver.php?id=amdxata.sys
http://www.carrona.org/drivers/driver.php?id=nvhda64v.sys
http://www.carrona.org/drivers/driver.php?id=nvlddmkm.sys
http://www.carrona.org/drivers/driver.php?id=rtl8192Ce.sys

BSOD BUGCHECK SUMMARY

Code:

Loading Dump File [C:\Users\John\_jcgriff2_\dbug\__Kernel__\070712-13322-01.dmp]
Built by: 7601.17835.amd64fre.win7sp1_gdr.120503-2030
Debug session time: Sat Jul  7 22:47:42.394 2012 (UTC - 4:00)
System Uptime: 0 days 0:13:03.705
BugCheck A, {fffffffffffffd20, 2, 0, fffff80002e5aeba}
Probably caused by : ntkrnlmp.exe ( nt!KeQueryValuesProcess+a0 )
DEFAULT_BUCKET_ID:  WIN7_DRIVER_FAULT
BUGCHECK_STR:  0xA
PROCESS_NAME:  GameClient.exe
FAILURE_BUCKET_ID:  X64_0xA_nt!KeQueryValuesProcess+a0
Bugcheck code 0000000A
Arguments ffffffff`fffffd20 00000000`00000002 00000000`00000000 fffff800`02e5aeba
BiosVersion = 0503   
BiosReleaseDate = 01/05/2010
SystemManufacturer = System manufacturer
SystemProductName = System Product Name
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨``
Loading Dump File [C:\Users\John\_jcgriff2_\dbug\__Kernel__\070712-14508-01.dmp]
Built by: 7601.17835.amd64fre.win7sp1_gdr.120503-2030
Debug session time: Sat Jul  7 21:24:04.624 2012 (UTC - 4:00)
System Uptime: 0 days 0:03:21.935
BugCheck 1, {7799137a, 0, ffff0000, fffff88004736ca0}
Probably caused by : ntkrnlmp.exe ( nt!KiSystemServiceExit+245 )
DEFAULT_BUCKET_ID:  WIN7_DRIVER_FAULT
BUGCHECK_STR:  0x1
PROCESS_NAME:  svchost.exe
FAILURE_BUCKET_ID:  X64_0x1_SysCallNum_3_nt!KiSystemServiceExit+245
Bugcheck code 00000001
Arguments 00000000`7799137a 00000000`00000000 00000000`ffff0000 fffff880`04736ca0
BiosVersion = 0503   
BiosReleaseDate = 01/05/2010
SystemManufacturer = System manufacturer
SystemProductName = System Product Name
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨``
Loading Dump File [C:\Users\John\_jcgriff2_\dbug\__Kernel__\070712-15022-01.dmp]
Built by: 7601.17835.amd64fre.win7sp1_gdr.120503-2030
Debug session time: Sat Jul  7 21:31:59.650 2012 (UTC - 4:00)
System Uptime: 0 days 0:00:13.962
BugCheck 19, {3, fffff800030076e0, fffff800030066e0, fffff800030076e0}
Probably caused by : Pool_Corruption ( nt!ExDeferredFreePool+a53 )
BUGCHECK_STR:  0x19_3
DEFAULT_BUCKET_ID:  WIN7_DRIVER_FAULT
PROCESS_NAME:  services.exe
FAILURE_BUCKET_ID:  X64_0x19_3_nt!ExDeferredFreePool+a53
Bugcheck code 00000019
Arguments 00000000`00000003 fffff800`030076e0 fffff800`030066e0 fffff800`030076e0
BiosVersion = 0503   
BiosReleaseDate = 01/05/2010
SystemManufacturer = System manufacturer
SystemProductName = System Product Name
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨``
Loading Dump File [C:\Users\John\_jcgriff2_\dbug\__Kernel__\070812-17581-01.dmp]
Built by: 7601.17835.amd64fre.win7sp1_gdr.120503-2030
Debug session time: Sun Jul  8 08:27:23.698 2012 (UTC - 4:00)
System Uptime: 0 days 7:57:23.633
BugCheck 18, {0, fffffa80040fc810, 2, fffffa80041fd49d}
Probably caused by : afd.sys ( afd!AfdCompletePollIrp+a0 )
DEFAULT_BUCKET_ID:  WIN7_DRIVER_FAULT
BUGCHECK_STR:  0x18
PROCESS_NAME:  plugin-contain
FAILURE_BUCKET_ID:  X64_0x18_CORRUPT_REF_COUNT_afd!AfdCompletePollIrp+a0
Bugcheck code 00000018
Arguments 00000000`00000000 fffffa80`040fc810 00000000`00000002 fffffa80`041fd49d
BiosVersion = 0503   
BiosReleaseDate = 01/05/2010
SystemManufacturer = System manufacturer
SystemProductName = System Product Name
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨``
Loading Dump File [C:\Users\John\_jcgriff2_\dbug\__Kernel__\070812-18626-01.dmp]
Built by: 7601.17835.amd64fre.win7sp1_gdr.120503-2030
Debug session time: Mon Jul  9 00:27:42.696 2012 (UTC - 4:00)
System Uptime: 0 days 15:59:53.007
BugCheck 50, {fffff8800705bdb8, 1, fffff80002e38110, 1}
*** WARNING: Unable to verify timestamp for win32k.sys
*** ERROR: Module load completed but symbols could not be loaded for win32k.sys
Probably caused by : ntkrnlmp.exe ( nt!KeEnumerateKernelStackSegments+28 )
DEFAULT_BUCKET_ID:  WIN7_DRIVER_FAULT
BUGCHECK_STR:  0x50
PROCESS_NAME:  System
FAILURE_BUCKET_ID:  X64_0x50_nt!KeEnumerateKernelStackSegments+28
Bugcheck code 00000050
Arguments fffff880`0705bdb8 00000000`00000001 fffff800`02e38110 00000000`00000001
BiosVersion = 0503   
BiosReleaseDate = 01/05/2010
SystemManufacturer = System manufacturer
SystemProductName = System Product Name
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨``