Ring Doorbell 1st gen not activating the mechanical chime

After upgrading the original transformer (16V - 10A) that came with the house with a new 16V 40A and still not being able to make the battery on the Ring Doorbel charge (or at least keep charge) I cannot make the chime work with it.I have tested the circuit with a doorbel button, shorted the wires with a screwdriver and even tried a camera doorbell from another manufacturer that a neighbor loaned me; they all work fine with the mechanical chime installed in the house.The last time I called Ring Support, I was told to add a resistor in series with my transformer/chime circuit to ensure 'enough resistance' is seen by the Ring Doorbell (1st gen) which of course didn't work.Since the doorbell I have has no brand or model, I cannot tell if it is supported explicitly or not; but I have sent photos to Ring Support twice and they haven't brought that up because they can't tell either. And since I don't know how this device closes the circuit to activate the mechanical chime, I cannot troubleshoot further.