Here is a link to the Ifixit guide on how to replace the motherboard in your clock. It is handy as it shows how to access the motherboard.
Given that you say most of the other functions seem to work and in the absence of a circuit diagram available online, at this stage it might be just as easy to inspect the motherboard for any obvious problems such as swollen or blown capacitors or stressed components (signs of heat or burnt).
XtremeMac Luna Motherboard Replacement
If you have any doubts about a particular component just post some close up pictures and hopefully someone will help you.
Adding images to an existing question