Thanks for the video. I believe I may be able to make an educated guess about the source of your problem (which as you admit yourself is extremely minor, so minor that I cannot see it on video), the reason being because I run a very similar setup. I have two GTX 670 2 GB cards (which are basically the same card as yours, but nerfed slightly) running in SLI. Overall I am very happy with my setup, but the biggest "problem" I have run into, and the reason I often regret not getting Radeon 7970's, is that the video RAM becomes a limitation in a very high end graphics scenario in my setup, even at 1920x1080, with my 2 GB of video RAM.
I created a video for you in Skyrim using Shadowplay. The reason I chose this game is because it is, by far, the game that most easily reaches the limits of what my setup can produce. I was most certainly NOT getting 60 fps during this entire test. The number of texture packs I'm running is absurd, and they are all the highest resolution packs I could find, so when I monitor my system, ENB is actually preloading something like ~10 GB of data (no joke) into my RAM and the actual video RAM usage itself when I'm outdoors will pretty much stay near 2000 MB the whole time. This consistently produces a noticeable stutter when I am entering a new area, or turning towards an object I have not yet "seen" (ie, my GPU has not loaded) and this causes a small stutter. It's been explained to me that the reason for this is that in this situation, the graphics card really only has enough room on the video card to store the textures I'm looking at at the time (because they're so large), hence, when I go to look at new objects, the video card and surrounding systems must quickly offload unneeded textures and load the ones it needs onto the card, and
relatively speaking, this is a slow process. That's why even the new GTX 970 comes with a beefy 4 GB of RAM despite only having about the same amount of power as my SLI setup.
https://www.youtube.com/watch?v=u8NadqSOi80
When it happens, it feels as if there is a strong "resistance" when I move the mouse. It's annoying, and to be fair, I went overboard with my mods and I plan on changing the whole setup relatively soon as all of my mods are about a year old.
I admit the fact that you're seeing this problem in Street Fighter and HL2 which are relatively low-res non-demanding games is very odd, but still, I hope this helps you confirm somehow that this is related to memory shuffling somehow. To me that would seem to be the case.
One thing I can ask is that you run a benchmark of your 840 in Crystaldiskmark. I also have an 840 and it's a damn solid drive considering how relatively cheap it was at the time it was released. If you aren't pulling somewhere in the vicinity of 500 MBps read, we have a problem. I know since you have sandy bridge you probably have at least two SATA 3 ports. You may have your drive plugged into the wrong storage controller, or there may be something else wrong somewhere.
Have you double checked your Intel storage controller drivers (what chipset are you running)? Did you have the Intel RST (Rapid Storage Technologies) AHCI drivers installed before you switched back to IDE? I would run your drive in AHCI mode, personally, although honestly switching between AHCI and IDE, you have already dodged a bullet (that can kill your Windows installation) IMO and switching back to AHCI would require a full reinstall, again, IMO.
Unrelated question: are you actually running your monitor at 120 Hz? If not, man, cap those frames at 60. All you're doing is using twice as much power as you need to.