New PC Build Troubles

I have another suggestion. Your memory, you ran Memtest and found errors on one of the sticks, did you test the same stick in a different slot. That may be worth doing as it might be picking up on a motherboard fault in the related circuitry. As the other stick passed Memtest you could also try running a test of at least 8 passes with the good stick in the other slot.

Memtest is not 100% and can miss minor faults. Running the PC on some new or borrowed memory may also be worth a try.

You could also try running Prime95 and Furmark.

Prime95 (32bit) - 25.11 Download - EXTREME Overclocking
Prime95 Setup:
- extract the contents of the zip file to a location of your choice
- double click on the executable file
- select "Just stress testing"
- select the "Blend" test. If you've already run MemTest overnight please run the "Small FFTs" test instead. (run all 3 if you find a problem and note how long it takes to error out with each)
- "Number of torture test threads to run" should equal the number of CPU's times 2 (if you're using hyperthreading).
The easiest way to figure this out is to go to Task Manager...Performance tab - and see the number of boxes under CPU Usage History
Then run the test for 6 to 24 hours - or until you get errors (whichever comes first).
This won't necessarily crash the system - but check the output in the test window for errors.
The Test selection box and the stress.txt file describes what components that the program stresses.

FurMark: VGA Stress Test, Graphics Card and GPU Stability Test, Burn-in Test, OpenGL Benchmark and GPU Temperature | oZone3D.Net

FurMark Setup:
- If you have more than one GPU, select Multi-GPU during setup
- In the Run mode box, select "Stability Test" and "Log GPU Temperature"
Click "Go" to start the test
- Run the test until the GPU temperature maxes out - or until you start having problems (whichever comes first).
NOTE: Set the alarm to go off at 90ºC. Then watch the system from that point on. If the system doesn't display a temperature, watch it constantly and turn it off at the first sign of video problems. DO NOT leave it it unmonitored, it can DAMAGE your video card!!!
- Click "Quit" to exit

It will be interesting to see if the hard drive is the problem after it passed the manufacturer's diagnostics.

If install is failing at final stages try accessing Device Manager during install to uninstall any devices in error to let installation complete, then install/update the device driver from the desktop: Device Manager - Access During Windows 7 Installation

Where did you get the Win7 installer? Did you burn it yourself? If so, confirm the ISO HASH and burn another at 4x speed with Verify using ImgBurn. Or write the ISO to flash stick using this tool with Win7 in the dropdown menu: Universal USB Installer – Easy as 1 2 3 | USB Pen Drive Linux to eliminate the installer.

This is not XP. I would not change out drivers which are already in the installer or quickly updated via optional Windows Updates after enabling hardware auto-updating, unless performance issues are traced to a specific driver: Automatically get recommended drivers and updates for your hardware.

If you bought new RAM, use that. What brands of RAM were they?