GUEST, KP...you say:

"...we know that each molecule of CO2 can absorb radiation at a certain frequency (14 micron wavelength) and that water doesn't absorb at that frequency."

and

"...its quite easy to calculate how much energy all that CO2 could absorb - its about 6E+20J (followed by 20 zeros) joules for every absorption cycle."

The trouble I see with that is: you are telling us how much energy the CO₂ can absorb/hold/release in the atmosphere, not the amount of heat it does absorb/hold/release. Not the same thing.

At 361 ppm, CO₂ is involved with a tiny portion of the total radiated heat, the rest passes through the atmosphere and makes contact with nothing.