Chosen Solution
So I had this game boy for along time but the ac adapter broke and after a lot of years a bought a new one but now the console is not charging at all… not even the red light goes on when I put the charger but the console still goes on and since the battery is dead it goes off right next
First of all, check the current output of the charger. If that value is equal or above the one on the original, then the battery is dead and you should get a new one.
I would recommend getting a new battery as Ciprian R said above. If that doesn’t work than it might be the actual connecter on the GameBoy. Take a quick peek inside it to see if there are any bent pins or any loose wires or such.