Random BSOD refers to ntoskrnl.exe

Jim, do you have any USB HDD attached? thest two, collectively indicating that a USB HDD is failing.

Event[1788]:
Log Name: System
Source: Service Control Manager
Date: 2012-09-07T23:00:50.650
Event ID: 7001
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: Dorie-HP
Description:
The DHCP Client service depends on the Ancillary Function Driver for Winsock service which failed to start because of the following error:
A device attached to the system is not functioning.

Event[1706]:
Log Name: System
Source: Disk
Date: 2012-09-07T22:52:05.720
Event ID: 11
Task: N/A
Level: Error
Opcode: N/A
Keyword: Classic
User: N/A
User Name: N/A
Computer: Dorie-HP
Description:
The driver detected a controller error on \Device\Harddisk2\DR2.

Let us know.

If yes, see that removing that one works or not.

If no, we may suggest you to enable driver verifier again, as the dumps are saying nothing specific

OK, then enable Driver Verifier.

Run Driver verifier for the next 24 hours or the occurrence of the next crash, whichever is earlier. When over, let us know, thet the subsequent dumps , if any.

Code:

......
*******************************************************************************
*                                                                             *
*                        Bugcheck Analysis                                    *
*                                                                             *
*******************************************************************************

Use !analyze -v to get detailed debugging information.

BugCheck 119, {1, 716, 701, 701}

*** WARNING: Unable to verify timestamp for atikmpag.sys
*** ERROR: Module load completed but symbols could not be loaded for atikmpag.sys
*** WARNING: Unable to verify timestamp for win32k.sys
*** ERROR: Module load completed but symbols could not be loaded for win32k.sys
Probably caused by : dxgmms1.sys ( dxgmms1!VidSchiVerifyDriverReportedFenceId+ad )

Followup: MachineOwner
---------
======================================================
1: kd> lmvm atikmpag
start             end                 module name
fffff880`03cb0000 fffff880`03ceb000   atikmpag T (no symbols)           
    Loaded symbol image file: atikmpag.sys
    Image path: \SystemRoot\system32\DRIVERS\atikmpag.sys
    Image name: atikmpag.sys
    Timestamp:        Wed May 12 06:54:19 2010 (4BEA0343)
    CheckSum:         00044ACB
    ImageSize:        0003B000
    Translations:     0000.04b0 0000.04e4 0409.04b0 0409.04e4

So, you are to update your graphics driver. Get it from AMD Support & Drivers.

Do a system restore to a point just earlier than the driver install.

Then install the driver following the method: Driver Install - Device Manager.
Point the driver update wizard to the downloaded driver.

Well done, Jim :)

Best of luck. I hope the problems will not return there.