No AC Power, Etcetera, when Adapter Plugged In

When I plug the adapter into the wall socket while not picking up the receiver, the screen says: "No AC Power".

There is also no dial tone when I pick up the receiver.

Yet, then I disconnect the adapter, the dial tone sounds.

Moreover, when I pick up the receiver while the adapter is unplugged, from the wall socket, there is a dial tone. I can plug the adapter into the wall socket, while holding the receiver, too, and the dial tone remains.

Any thoughts on the problem and a fix?