There would be a lot of cost in materials and installation to do this. You would have to bury the lines below the frost line if you live in an area that freezes. Here in MN, that is around 5-6 feet down in most places. If it gets cold enough, especially with no snow, frost goes deep. It is just not a cost-effective way to cool a PC. You will also need stronger umps than usual that can push suck a large volume of water and be able to lift it out of the ground.
Already been done, and very easily. Have to look through my posts but I believe it was @Shrimpbine ? who just hooked up his water faucet from his sink to his cpu pump and exited to the drain. So basically you have constant earth temp coolant that never heatsoaks.
Alternatively if you live in a place with lots of groundwater that isn't too deep, you can do away with laying lots op tubing in your yard and just pump up the usually colder ground water into a vat for heat exchange.
This should prevent condensation as well as you can control the temperature in the vat by triggering the pump with a thermostat.
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