Random Blue Screen Error: 0x0000003b

When did this behavior start - did you recently add or remove any hardware or software?

Is the BCCode always the same? How frequently do you get a bugcheck?

Can you upload the contents of c:\windows\minidump to your SkyDrive, and provide a link?

You got bugcheck 0x3b - that's  SYSTEM_SERVICE_EXCEPTION.  The exception referenced is STATUS_ILLEGAL_INSTRUCTION - "Illegal Instruction" - "An attempt was made to execute an illegal instruction."

The illegal instruction could be caused by a corrupted image (executable module) on disk, or memory corruption.  Consider running chkdsk on your drives, as well as SFC /SCANNOW.

General guidance for dealing with bluescreens:

Consider running chkdsk on all partitions.  Let chkdsk complete on each partition and see if that helps.

Also consider running SFC /SCANNOW.

If you boot into safe mode, do you still experience bugchecks? What about if you do a clean boot, or device clean boot?

Consider testing memory with Windows Memory Diagnostic or memtest86. Note that memory that passes tests is not necessarily good memory - it just hasn't failed a test.  Consider systematically eliminating RAM from the system - run with a couple of modules for a while, and see how things go. Then try the other modules.

Other common suggestions include ensuring drivers are up to date, as well as ensuring that you're using the latest BIOS. 

It can be helpful to use Driver Verifier.  To enable Driver Verifier... start->verifier.exe->OK->Create standard settings->Next->select driver names from a list->Next->sort by Provider->select all non-Microsoft drivers->Finish, and OK your way out of the dialog.

Then, reboot and use the system as you normally would, and wait for a problem.  In the event that the system does not boot completely after enabling driver verifier, boot into Safe Mode and run driver verifier, and tell it to delete the changes.

Wait for a bugcheck to occur after enabling verifier as described, and then upload the dump to your SkyDrive, and provide a link.

3b is usually a graphic's driver (display adapter/video driver), other possibilities include but are not
limited to antivirus/antispyware/security programs and even memory (mapping).

BCCode: 3b    0x0000003b

Cause

This error has been linked to excessive paged pool usage and may occur due to user-mode graphics drivers crossing over and passing bad data to the kernel code.


BCCode: 3b    0x0000003b  <-- read this
http://www.faultwire.com/solutions-fatal_error/SYSTEM-SERVICE-EXCEPTION-0x0000003B-*1074.html

============================================================

Vista and Windows 7 love updated drivers so here is how to update the major ones.

References to Vista also apply to Windows 7.

This is my generic how to for proper driver updates : (update video/display driver and BIOS)

This utility makes it easy to see which versions are loaded :

DriverView - Free - utility displays the list of all device drivers currently loaded on your system.
For each driver in the list, additional useful information is displayed: load address of the driver,
description, version, product name, company that created the driver, and more.
http://www.nirsoft.net/utils/driverview.html

For Drivers check System Maker as fallbacks and Device Maker's which are the most current.
Control Panel - Device Manager - Display Adapter - write down the make and complete model
of your video adapter - double click - Driver's tab - write down the version info. Now click UPdate
Driver (this may not do anything as MS is far behind certifying drivers) - then Right Click -
Uninstall - REBOOT this will refresh the driver stack.

Repeat that for Network - Network Card (NIC), Wifi, Sound, Mouse and Keyboard if 3rd party
with their own software and drivers and any other major device drivers you have.

Now go to System Maker's site (Dell, HP, Toshiba as examples) (as rollback) and then Device
Maker's site (Realtek, Intel, Nvidia, ATI as examples) and get their latest versions. (Look for
BIOS, Chipset and software updates at System Maker's site while there.)

Download - SAVE - go to where you put them - Right Click - RUN AD ADMIN - REBOOT after
each installation.

Always check in Device Manager - Drivers tab to be sure the version you are installing actually
shows up. This is because some drivers rollback before the latest is installed (sound drivers
particularly do this) so install a driver - reboot - check to be sure it is installed and repeat as
needed.

Repeat at Device Makers - BTW at Device Makers DO NOT RUN THEIR SCANNER - check
manually by model.

Manually look at manufacturer's sites for drivers - and Device Maker's sites.
http://pcsupport.about.com/od/driverssupport/ht/driverdlmfgr.htm

Installing and updating drivers in Windows 7 (updating drivers manually using the methods above
is preferred to ensure the latest drivers from System maker and Device makers are found)
http://www.sevenforums.com/tutorials/43216-installing-updating-drivers-7-a.html

If you update drivers manually then it is a good idea to disable Driver Installations in Windows
Updates, this leaves Windows Updates ON however it will not install drivers which will usually be
older and cause issues. If Updates suggests a new driver then HIDE it (Right Click on it) and then
go look for new ones manually if you wish.

How To Disable Automatic Driver Installation In Windows Vista - Drivers
http://www.addictivetips.com/windows-tips/how-to-disable-automatic-driver-installation-in-windows-vista/
http://technet.microsoft.com/en-us/library/cc730606(WS.10).aspx

Hope this helps.