BSOD mainly when playing games, some tests already run.

Ken is a very experienced and efficient debugger. It is all possible that his suggestion is valid. If you want us to assist you , I would ask you to upload your MSINFO32.nfo file, which will give us some more info about your system.

1. Click on the start button
2. Type "msinfo32" (without quotes) in the search bar of the start menu, click the resulting link. It will open the System Information window.
3. File>Save. In the "File Name" filed, put "MSINFO32" (without Quote), give the save location to desktop, and click the "save" button.
4. Give the time for processing, it will save a .nfo file on your desktop.
5. Zip it, and upload it following the instruction.

Do some Disc checks.

1. Update your SSD's Firmware
   OCZ Agility 3: OCZ Toolbox: Firmware & BIOS Updates
   Samsung 840 Pro: Magician Software (Software) (ver.4.0)
2. Re-seat the sata and power.
   
3. Run chkdsk /f/r, following the option two of the tutorial Disk Check
4. Seatool for dos: SeaTools | Seagate download
   
   • Burn it in a blank cd. boot from the CD, click on "Accept", wait for it to finish detecting the drives, then in the upper left corner select "Basic Tests", then select "Long Test" and let it run.
   • You can use Win32 DiscImager to create a bootable USB and run Seatools for DOS. Follow this post to know how to make a bootable Seatools USB.
   
   (Steps 3 and 4 are for the HDD only)
5. Post screenshots of all the SSD's and the the HDD using CrystalDiskInfo - Software - Crystal Dew World

Uninstall NoSleep HD.

Boot into BIOS ... make it sure that the Storage controller mode is set to AHCI mode or IDE mode.

Get rid of intel rapid storage. First uninstall it from Control Panel > Programs and Features. Then Uninstall the driver from device manager.

1. Right click on "my computer" icon and click "manage" on the context menu.
2. It will open the "computer management" window.
3. Select "Device Manager" in the left pane, It will list all the existing devices up.
4. Expand "IDE ATA/ATAPI controllers" by clicking on the triangle in front of it.
5. Select one Intel device item under it, right click, uninstall.
6. Continue the process for all Intel items under "IDE ATA/ATAPI controllers"
7. Now restart the computer. At restart, windows will auto configure the appropriate native system driver.

And a few more things too, as the last crash dump we checked was a stop 0x124.

Test your RAM modules for possible errors.
How to Test and Diagnose RAM Issues with Memtest86+
Run memtest for at least 8 passes, preferably overnight.

Stress test the Graphics Card using Furmark.
Video Card - Stress Test with Furmark

Stress test the CPU.
Hardware - Stress Test With Prime95

Is the computer hot? Report us the heat of the computer after a couple of hours of your normal usage. Upload a screenshot of the summery tab of Speccy.

Check if the Power Supply Unit (PSU) supplying adequate power to the computer or not.
eXtreme Power Supply Calculator
Also let us know about the wattage of your PSU.

Good :)
Only one thing is missing there ... the screenshot/snapshot of Speccy.

And, let us know the results of seatools test when done :)

Have you used Win32DiscImager rightly, as instructed? If so, have you used the boot menu key of the BIOS to select the USB device to boot from?

If both the answers are positive, I would suggest you to try a bootable CD.

Temps are not any issue there.

Try to re-burn the USB stick?
It is always better to have an ODD drive ... it works in bad times :)