A transformer has more than one winding so at least three connections if one is shared or four if not. A component with a single winding (and two connections) is an inductor.
With that bit of pedantry out of the way, in nearly all cases, it doesn't matter which way round you connect an inductor.
Before you do *anything* to the board, look closely at all the solder joints with a magnifier to see if you can find any evidence of the broken off wires.
For us to help you figure out the connections, we'd need to understand the circuit, which means we need good, large, well lit, in focus photos of *both* sides of the board, clear enough to read the tiny part numbers.