What sort of power supply/transformer does it have? Switched mode, linear?
In a linear power supply, the transformer will be the first thing in the circuit, after the fuse and mains switch. The transformer will be a big lump of iron, which may or may not be directly soldered to the PCB.
In a switch mode power supply, there will be a bridge rectifier, big smoothing capacitor and some transistors before the transformer. The transformer will be fairly small and will directly mounted to the PCB.
If it's a linear power supply, then you could try powering the transformer on its own, with nothing on the secondary. It's possible the transformer has developed a shorted turn, which is responsible for the fuse blowing. If it works, then you know it's something on the secondary side, otherwise you need a new transformer.
In a switched mode power supply, it's more complicated. Check the rectifier and main filter capacitor first. If they're fine, then it's most likely one of the switching transistors has failed short circuit.