Civilization – Problem with stretched sheep in Civ V! What to do

Since I've been there and my heart goes out to you, I feel inclined to take a stab. Such debug can be a nearly endless process, and I'm not an authority on all aspects (but I do have 10+ years building and working on computers). Some additional options and debug to try:

Debug/Questions

1. When the computer crashes with Skyrim or Warcraft, do sounds on the computer stop/skip, or do they appear to continue normally? Can you press the CAPS LOCK or NUM LOCK keys on your keyboard and see the light turn on/off? These are indications that your computer is alive, but the graphics are dead. This would mean a new graphics card (different brand or new version) would be worth trying. Make sure you buy from a place with a good return policy (if possible).

2. For whatever display output you use (VGA, DVI, HDMI, etc), can you try a different one? Moving from DVI/HDMI to VGA or vice versa stresses different parts of the GPU in some cards and may provide insight or a temporary workaround.

3. Does your motherboard support integrated graphics? If so, try running the games in question with the GPU uninstalled. This presents it's own challenges in that integrated graphics are often under powered - but it may provide a useful reference point.

4. As Jupotter suggests, try the card in a different slot. Various scenarios can cause one slot to be bad temporarily or permanently - although this seems less likely given the failure mode you describe.

5. Check that the OS settings for the GPU power management are all set to "Max Performance". I have observed cases in the past, particularly with Warcraft, in which severe graphics corruption resulted from the GPU attempting to enter "low power mode." However, typically for desktop computers the default is already "Max Performance".

I usually don't have this affect when installing mods like Optifine, however sometimes they just fail to completely install.

It's a longshot but perhaps utilising a texture pack will fix the problem.

Otherwise try reinstalling Minecraft and the mods - remove all files under .minecraft from %APPDATA%, just remember to copy over your saves. Once Minecraft has downloaded all the files it needs, re-install your mods.