What mean two dots on same transformer winding
That means you're out of luck with that diagram, they really screwed up. The direction of the first coil will not be able to be determined from the schematic. You could pull it out and run a waveform from a signal generator to determine the directions. 

If the coil from 7 to 5 really is open (and you believe the schematic) the transformer is probably bad (or the schematic is wrong).