I would try cleaning the contacts between the buttons and the chip and the buttons themselves. I recommend Isopropyl alcohol to clean it. You will have to pretty well dismantle the Tamagotchi to do it, so make sure you're comfortable with doing that first.
Beyond that though I'm not too sure what else to try.
I agree with Nazotchi, cleaning the contacts and buttons may help. However, if you have a broken tama, then I recommend swapping buttons with it. My V5 Celebrity was having a similar problem, so I swapped buttons with a broken V1 and it worked! I also recommend tightening the screws on the circuit and the back as much as you can when you're done cleaning it.