Help with random BSODS please

Hi everyone,

I've often referred to Tom's hardware for advice in the past but this is my first ever post, so be gentle, i'm at my wits end with this problem and need some of your expert advice!

Firstly, on a scale of 1 to 10, my PC technical knowledge is at about a 6, so speaking in plain english would be a huge plus please.

Here's the problem:
About 4 months I upgraded mine and my wife's PC's with the following new parts:

-Asus Z87 Motherboard
-Intel I7 4770k 3.5ghz
-Samsung 2tb hdd

We kept the following parts from our previous builds:

-Radeon HD 6970 2GB gpu
-Corsair TX850 psu
-8gb (2x4gb) Corsair Vengeance DDR3 RAM

Since the upgrades, my pc has been suffering from random BSOD's at random times with little to no consistency that would hint at the cause. My wife's identical build has worked flawlessly since day one.

Both PC's are used for gaming daily.

What we've tried so far:

-Switched graphics cards to see if the BSOD's stop (no affect)
- Removed the CPU, properly cleaned it, reapplied the thermal paste (using arctic silver) and re-sat the cpu onto the board (no affect)
- 2 Clean installs of Windows 7 64-bit (no affect)
- Ran disk checker in the command prompt to check for problems (no problems found)
- Re-sat the graphics card (seemed to stop the bsods for about 1 week but then they started persistently again)
- Re-seated the RAM sticks (no affect)
-Updated my bios & firmware as it was quite outdated (hugely helped in slowing the amount of BSOD's I get, but they still occur once every 2- weeks or so, down from 2 or 3 per week).

I havn't yet ran a memtest as the ram worked fine in my previous build less than 1 hour before being installed onto the new motherboard, though I do intend to run one soon just to eliminate all potential causes.

I currently have 21 bsod info's in BlueScreenView, though i'm not sure of the best way to share them with you guys, but all BSOD bug strings have been fairly random until recently after updating the mobo firmware where not only did the bsod occurances greatly reduce as mentioned above, the 2 i've experienced both share the same bug string: 0x00000124.

Before that i've had:

12 x 0x0000003b
2 x 0x1000007e
2 more (4 in total) x 0x00000124
2 x 0x000000d1
1 x 0x00000024
2 x 0x0000000a

Additionally:
CPU and GPU temperatures are all well within the recommended temps both in the manuals and online, plus my case is huge and full of fans so i'm fairly confident nothing is getting hotter than it should.

So after loads of research online from a few others who've had the same problem, nobody has really said anything 100% conclusive as to the cause of the problem, however a faulty motherboard has been brought up a few times... But since the Z87 isn't cheap I don't fancy buying a new one just to test it only to find out I was wrong, and returning it under warranty could take weeks so i'd like to exhaust all options first.

I'm not entirely new to pc construction having built our last 2 builds that worked fine, but this issue has me completely and utterly stumped, so I felt the time was right to seek help from you guys in this awesome community!

So please ask for any additional information you need from me to help rid my PC of this terrible bsod circle, although they occur less now, I don't feel as though I can trust my PC enough to not BSOD on me in the middle of working on a project etc, so i'd really appreciate if you can help me resolve the issue once and for all.

EDIT: My last BSOD was today, about 2 hours ago, before that the last one was on the 2nd of June. Both of the recent BSOD's occured whilst gaming. The bsods have slowed down alot with the firmware update, but why are they still occuring at all?

Kindest regards,
MoonSponge