Random BSOD. Reports attached

Can you post the CPUZ CPU tab?

The CPU, RAM and NB or equivalent voltage readings obtained from BIOS are important, include these in your next post.
If these are set to Auto, let us know, if it doesn't display the current voltage then increase them by the smallest amount possible so you can see the current voltage.

A LITTLE CLARIFICATION REGARDING GANGED/UNGANGED MODES & SINGLE/DUAL CHANNEL CONFIGURATION.

Ganged Mode and Unganged Mode are not the same as Single Channel or Dual Channel configuration.

The Ganged/Unganged mode refers to how the RAM Modules actually talk to the Memory Controller(s) on the CPU.

Single or Dual channel configuration refers to how the RAM is installed in the memory slots on the motherboard. With one stick of RAM you are using single channel mode. With two sticks of RAM you can run in either Single or Dual Channel mode depending on how you fill the Memory Slots on the motherboard. If you use three or four sticks of RAM you will be running in Dual channel mode.

On Gigabyte's AMD Boards there are two channels, each of which address one of the two memory controllers on the AM3 CPU. Channel 0 normally equals the Memory slots on the motherboard identified as DDR3_1 & DDR3_3 whilst Channel 1 normally refers to DDR3_2 & DDR3_4.

If, for example you have two sticks of RAM and you put them into slots DDR3_1 & DDR3_2 you are running in Dual Channel Mode, each stick of RAM talks to its own Memory Controller. If you put the RAM into slots DDR3_1 & DDR3_3 you would be running in single channel mode, where both sticks of RAM are only talking to one of the Memory Controllers. (You would need to double check with your motherboard's own manual for correct Memory Slot Channel configuration)

Ganged Mode is where you utilize both Memory Controllers on the CPU as a single unit giving you a single 128 bit channel. (You may not be able to run RAM faster than 1333Mhz in this mode. I haven't been able to with either the X4 965 or the X6 1090T.)

Unganged Mode is where each of the Memory Controllers on the CPU work independently and equals 2X64 bit Channels. (I can run my RAM at 1600 Mhz only in this mode)

More information from the same site on the same issue.

AMD AM3 CPU's and Memory Speed Issues above 1333 Mhz.

Let us know if they are different than you posted.

If your CPU NB VID Control, page 40 in your motherboard manual, is 1.1v then bump it to 1.2v.
DRAM 1.5v.
Unganged mode.

Run memtest86+ starting with Stick 1 - Slot 2.
Let it run for 8 passes, overnight is easiest.

If this passes then run memtest86+ with Stick 1/2 - Slot 1/2, this is dual channel configuration.
Let it run for 8 passes, overnight.

Let us know the results.

Next time you open the case, check the lower left corner of the motherboard for the revision number, should be 2.0, 2.1 or 2.2.

The link is a good read, yes you need to get the system stable then you can try tightening the timings.

Have you ever updated BIOS before?
If not, can you get help from an experienced friend or take it to a shop?
Flashing BIOS is risky for anyone, you have to accept that it can leave your motherboard un-usable.
A quick web search found mention of pre-F3 BIOS being 'buggy', they are recommending F3 and F4, F5a is a beta version and not recommended.
If you do decide to flash your BIOS, use QFlash not the @BIOS Windows based utility.

In searches today I found several references to your motherboard having high NB, North Bridge (motherboard not integrated CPU) temps, causing some problems. Check the temp with SpeedFan.

I have rev 2.0, an old one unfortunately. Fell asleep last night before I had a chance to get the MemTest running, will run the test some point today and start using the work laptop instead.

I have updated a BIOS before, but using EZ-Flash and not Qflash but I assume the two are a similar concept. Will update to F4.

Speedfan reported something at 80C (I assume my motherboard is missing whatever sensor Temp3 is trying to log). Had a feel of some of the bigger components inside and nothing felt at 80C. Attached the screenshot.

HDD temps average out a little above 50 after some use (got 4 packed closely together, I'll take one out soon for a different computer and maybe install a front case fan). My nVidea Geforce 7900GT idles around 47 and 50. The GPU has always run a bit hot so I think it's okay. Ambient temp is pretty cold though, I'd guess around 20

Qflash uses a USB memory stick, CD or floppy, you can search the Gigabyte forum for info on it.

I would guess that 80 degreeC is a missing sensor.

Must be Temp1, which is cool for the mobo NB. 50ish is pretty warm for HDDs, the front fan will help them.

50 for a GPU is good.

Let us know how the memtest86+ goes.

Bump the CPU NB VID Control to 1.3v with Stick 1 Slot 2, set in unganged mode, if you get an error stop the test, bump the DRAM voltage to 1.6v, run test again.

If this doesn't pass I would RMA the RAM.

If it does pass, leave settings as they were when passed and put the other RAM card in, run memtest again, stop if you get any erors.