I still want to go back to the transformer. It just sounds exactly like the correct symptom for a short from the primary to the rectifier filament winding. When you measured from the rectifier pins to the primary (or AC line cord with the switch closed) did you put your ohmmeter on it's higher ranges to check for high resistance shorts? You probably did, but I am at a loss to explain this any other way. The only other thing I can think of, and I've never seen it before, is a transformer short that is only there when power is applied.