Cold water runs for a few seconds and then stops. . .
you MAY have a chunk of stray solder in the lines. When the flow brings it up to the small spot in the line,it clunks and shuts off the flow. Only way is to take off pipe at where it goes from large to small and flush it adequately,,,might even take off the supply to cold faucet,,,might be just right size NOT to go thru faucet. Turning off the faucet lets gravity drop it back down and water flow brings it back up to the stick point!! Messy job but somebody has to do it.