Detect damaged SMD capacitors
Detecting ceramic SMD capacitors with a multimeter is going to be very difficult, basically impossible in a practical sense.  Forgettaboutit.

Capacitors look like opens at DC, which is what multimeters measure.  You can try inspecting every one with a jeweler's loupe and looking for cracks in the caps and their solder joints, but the chances of seeing even a truly cracked cap are small.

Ceramic caps aren't the likely suspects when the board fails.  Electrolytic caps are much more likely to fail, and some of the failure modes are visually obvious.  You say you only have SMD caps and later say they are not electrolytic, but I am not convinced you understand that SMD and electrolytic are orthogonal and how to spot a SMD electrolytic.  Look for anything that is roughly cylindrical and check if the top is really flat.  As tcrosley said, the larger electrolytic caps have scoring in the metal at the top so that they fail in a controlled way if they rupture, and are less likely to take other parts with them.  Replace anything that looks bulged, it doesn't need to be outright ruptured.

Still, the chance of finding a fault on something as complicated with sophisticated construction as a modern graphics card by using a meter and visual inspection is slim.  Unless you value your time at pennies/hour, you'd be better off just getting a new graphics card.