Please explain where in the circuit the ammeter is wired. An ammeter on the input will measure how much the entire transformer is drawing from the mains. Is that where you have the ammeter wired? An ammeter on the output will measure how much current is being used by a load. Since you need to ensure that there is no load on the transformer during your test, any indication of the output ammeter is irrelevant.
I need you to disconnect all the wiring (including any test equipment and/or meters) from all the binding posts and tell me what voltage you measure between posts A and B. Those posts are not under control of the circuit breaker inside the transformer. Then we can begin to see what the other secondary coils are doing.
Eventually, after you tell us that info, we can proceed to taking off the cover and using the voltmeter to find out if the circuit breaker is opening due to an internal problem, or if it's just not closing completely.
Do not be concerned about dangerous voltages, or burning down any houses. You can do these tests safely and have the satisfaction of learning how it works, and of knowing how to fix it.
Here's the diagram. As you can see, it's going to be easy to trace.
http://pictures.olsenstoy.com/...ansfmr%5Cps1032a.pdf