If the door bell push button is outside then it is likely the contacts are not too good - that is why the original bell probably used 24 or higher voltage (likely AC) to overcome this. Take the cover off the button and lightly sand or file the contacts until you have shiny metal again. Do the same with the screws and wires that are held by the screws. Finally, give it a spray of wd40 and reassemble. Test again. Hopefully it will work now. If you do not feel confident doing that a new door bell push button is probably not that expensive and you would only need to clean the wires where they meet the contacts. Finally, be careful with the wires. Electricians leave little extra and they will very likely be solid core and can break easily.