Transformer has continuity but no power on secondary coil
Your update tells me that your initial statement "...110V Ac is present to the terminals that supply power to the transformer..." is misleading. It implies that you are measuring at the transformer terminals - which you are not.
It is clear to me, that there is some safety circuit between the board terminals (were 110V comes in), and the transformer's input terminals.
Your safety circuit is detecting an unsafe condition and disabling power to the transformer primary terminals.
There is nothing wrong with the transformer.  Most likely, your power output transistors are shorted/blown, causing the safety circuit to remove power to the transformer.