It does sound like your transformer has fried. This is a very rare problem, but it can happen.
In the USA, the primary side of the transformer is designed for 120 VAC at 60 Hz. I'm assuming that you are in Europe because you are using a 50 Hz transformer.
In any event, you can definitely replace it. These were large and rugged transformers that were made by the Electrical Windings Co in Chicago, who specialized in producing transformers for the local pinball factories. If possible, you should try to find a used transformer of the same type, perhaps from a salvage parts game that someone is selling.
These transformers rarely go bad, so it is possible to get one from a game that was scrapped for other reasons. Because of the very high output current that these transformers need to supply, I think finding a used factory original is the best way to go.
While it is possible in theory to replace your game transformer with a new one, it can be challenging to find a new transformer with the necessary output current. As far as I can tell, the original Williams EM transformer could supply at least 20 amps at 6 volts, and 15 amps at 28 volts. So, if you are going install a new transformer, it would need to provide this kind of output power.
- TimMe