As this TX is basically directly connected to bridge rectifiers that would be my first port of call unless there is also some sort of surge device (MOV etc) ACROSS the secondary winding? There really is very little else that will cause a catastrophic failure such as this.

I don't have the schematic for X-Files but looking at Star Wars that came out the same year there is a fuse between the bridges and the transformer, wouldn't they blow if it was overloaded?
The only thing I could find without a fuse was the Backbox fluro, could that be the cause?