Hui, First of all if your system is hard wired you do not have a Din. I would start with the basics. Check you push button. Take it apart and check for corrosion, or signs of pest, (old spider webs/Eggs, bugs, or anything else that could cause a short circuit in it) If you have more then one push buttion check the other one.
Then check your transformer. You need a meter to do this check to see if the output is what it says on the transformer. (1.5,3,6,9,12 Ect.. Volts) If this is ok then check the door bell in the house. there should be a Red/white twisted pair of wires comming from the transformer, Take a wire and go from the red wire to the white wire coming from the doorbell button. It should ding.
My drawing isn't the greatest, but I hope you can see the basic's of a door bell wiring method. Don't worry about doing this while it is hot, You will not get a shock that will change your hair do for life. Let me know how you made out. Tim