My GPU stops suddenly and get black screen

Of course only one card was maxing out the single GPU, you can't run SLI with different GPU cores.

Save up and get another GTX 560 Ti if you want to increase triple monitor 3D performance too. The only ability you get by adding a lower performance graphics card is the ability to use three monitors, that's it.

You can also use a slower card to perform the PhysX rendering. Also, if you use any CUDA-specific applications, you can offset them to one particular GPU if you needed to.

If your second GPU happens to be SLI-compatible with the first one (as with Crossfire, which only happens when they share the same GPU core), when SLI/Crossfire is enabled, your performance will be limited by the slower card (or rather, the card with a lower amount of memory or lower clock frequency).

If you're able to take and store screenshots after the monitor goes to sleep, then the GPU isn't crashing. Windows 7 can't render frames without the GPU working.

It looks like you used to have a problem with heat or partial failure of the GPU causing reliability issues, thus the TDRs. But since you're no longer getting TDRs after underclocking and increasing the TDR timeout, that tells me that your GPU is now working well enough to be stable.

If you disable the TDR timeout, your PC would totally lock up (no ability to take screenshots or hear audio, etc) every time the GPU crashed, and it would stay locked up indefinitely or BSOD and you'd have to reboot. Similarly, if you're not getting BSODs when you do get TDRs, then your GPU is recovering from the crash successfully.

So this seems to be strictly limited to the display output path and has nothing to do with the "processing" part of the GPU. It could be:

• The cable itself (or the connection to the port header on either side) might be failing.
• Could be a problem with your monitor.
• The display chip on the graphics card (there's a separate IC for, e.g. HDMI or DisplayPort codec) might be failing.
• The header itself (the "port" interfacing between the innards of the graphics card and the cable) might be failing.

Things you should try:

• With the same monitor, try running off of your Intel 4770 CPU's integrated graphics, by plugging your monitor into the motherboard (only - do not plug anything into the Nvidia card).
• Try a different monitor if you have one.
• Try a different Nvidia card if you have one.
• Make sure you're running the latest Nvidia Game Ready drivers, in case it's a software or firmware issue.
• Put your (same) Nvidia card into a different PCI Express slot (but plug the monitor cable into the Nvidia card, not the motherboard).
• If your Device Manager shows an Intel HD graphics device even while you have your monitor cable plugged only into the Nvidia card, update your Intel graphics drivers for your processor from intel.com.
• Try running Ubuntu off of a live CD or a USB thumb drive for a while to completely eliminate software as the culprit.

If swapping the Nvidia card or running off of the Intel HD graphics solves the problem, it's very likely to be a failing Nvidia card (some part of it; but it doesn't really matter which part because it's not like you're going to break out a $10k+ microsoldering kit and start physically repairing the traces, are you?).

If the problem persists with the Intel HD graphics only (with the Nvidia card playing no part in the display output path), it's very likely either the monitor cable, or the monitor itself going bad.

If the only thing that fixes it is running Ubuntu, it's very likely to be a software issue -- either a bad driver, bad configuration (of display timeout, etc.), or even a virus/malware in your Windows installation.