[Mondial]

You also may want to carefully clean the pins of the tubes that do not light. The loctal tubes are known to get corrosion on their socket pins, leading to poor contact and bad connections. It is highly unlikely that you would have four tubes with burned out filaments.

If the transformer leads are in good condition, it might be best to leave them alone. Removing the transformer and trying to replace the wires will probably do more harm than good, since you would have to disturb the delicate connections to the high voltage winding.