Folks this is another of the situations that happens occasionally where a lot of people are showing really good intentions in offering suggestions, but I fear the OP may be getting overwhelmed by all the posts. I would respectfully suggest we let PB work with the OP to sort this one in a methodical fashion.
Roger, don't turn the amp on again until PB posts some guidance. At this point the transformer is probably just fine, but a short somewhere else in the circuit is forcing it to draw way too much current when you turn it on. Eventually that will fry the transformer, and we need to figure out where the short is before running it for any duration. Now that you have resoldered a lot of the connections your best bet might be rechecking all of the resistances and posting any deviations.