[LHaven]

OK, when I opened the photo into its own tab, I got much more detail. (I'm so happy mine is plumbed in red and blue pipe instead of all white.)

I think what I am seeing is this (image, properly erected). The red is hot, the blue is cold and the green is bypass. The hard part was seeing how the hot tube is connected between A and B, so if you just assure me that it is, then I understand the flow here.

What I would suggest is that you turn the hose feed on, then pop the pressure relief valve on the outside of the heater. That will tell you whether cold is feeding into the heater. I'm guessing it won't be, because regardless of whatever you have done to the heater, there is a direct blue path from the left side of the photo to the rightmost blue blob (above the heater) that feeds something and doesn't touch the heater at all; and yet you claim that no cold water is running anywhere. (Did you check the toilet and the outside faucet?)