For the water to flow without a pump, you have to depend on "convection flows". Basically, warm water will rise, cool water will sink.
Convection systems usually use huge pipes or ducts, because the flow is going to be very slow, but also will involve a very large volume of water.
Convection cooling is not going to work very well with quarter-inch tubing. You'd probably have to move up to 1-inch or even larger to get enough mass-flow.
One of the big problems here is your heat-output radiator. Most CPU-cooler radiators use small-diameter pipe in the radiator, and that will slow down the convection flows. You'd likely have to use a radiator with 1" tube to match the water lines, or two or more of the usual small-tube radiators in parallel. The warm water should enter the top of the radiator and the cool water will exit the bottom.
Since this depends on very gentle water movement, any rough spots inside the CPU cooler plate will cause a lot of turbulence and slow the water down. Therefore, the CPU cooler plate should have large, smoothly polished channels inside.
Since convection flow depends on gravity to work, it is severely dependant on tube arrangement. If you have loops in your hose, or a high spot in the middle of a hose, that will very likely stop the whole thing from working. Also, you can't have air pockets anywhere in the system or it won't work.
Since cool water sinks, the cold-return should be lower than the hot-output from the CPU plate. This way as the hot water rises out from the CPU plate the cool water flows in underneath it.
Since there is no pump, you'd need to mount the water tank up high, possibly as high as or higher than the radiator in the top of the case. The tank is attached with a single line to the highest point in the loop. This way when the tank is full the convection loop is also completely full of water, without any trapped air in the radiator or lines.
The general flow works like this:
1. Turn on computer
2. CPU cooler plate slowly warms up.
3. Water in CPU cooler plate warms up.
4. The water in the cooler plate becomes less dense as it warms, and so it becomes buoyant and starts rising up the hot-output tube.
5. Because this is a closed loop with no air gaps, as this water rises it very gently pushes on the water throughout the loop. This is where large tube size and a smooth flow channel is important because when the computer is first turned on the water has to overcome the huge resistence to flow all along the convection path.
5b. If the tubing is too small or there's too much path roughness, the friction may be great enough that the water doesn't really start moving right away, until the CPU plate gets fairly hot and most of the hot-output column is warm. Maybe then there's enough buoyant water to get the flow moving... but if the path is still too small and rough, the CPU will just overheat because the convection flow is either not moving or is way too small to do any good.
6. If all is going well, the rising warm water pushes the cold water above it up, pushes the cool water through the radiator loops, and finally pushes some cool water down the radiator output and into the bottom of the CPU cooler plate, under the warmed water.
7. This cool water entering the bottom of the CPU plate then warms up and also becomes less dense, and the cycle continues.
8. As the water warm rises up to the top of the radiator, it warms the radiator fins, which start a second convection flow of air through the fins. The air takes away the heat, and the water cools, until it exits the bottom back to the CPU plate again.
8b. If the radiator is packed into a tight space, there may not be enough natural airflow through it to remove heat quickly enough. You need large volumes of air to naturally flow over the radiator. If the water cannot be cooled quickly enough, the convection cycle will stall out because the water is still hot and is still floating as it comes out the bottom of the radiator. This warm water balances the warm water over on the "hot" side, and the flow stops.
...in short, this is quite a job to do right..
<font color=green> The second time is always better than the first 
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