Transistor replacement for power supply
Failure of the switching transistor in this type of power supply is not uncommon. Similar problems can be found in monitor and TV supplies.

The most common cause is that the peak voltages for some components are rather low. They are just enough but one or two spikes and they are gone.

The IFRS730 has only a Vds limit of 400 V (See datasheet) where in this kind of application a Vds of 600V is to be preferred. Therefore the FDPF8N60ZUT proposed by Seth is a better alternative.

It would go to far to explain the complete working of the powersupply but on top of the N channel mosfet replace also C1 by a 630V type and replace furthermore D1 -D4.  If F1 is a soldered in type of fuse make sure to replace it with the same value.

Warning.

You are working on the mains side of the power supply. Disconnect the supply from the mains when working on it and wait a couple of minutes before you touch the circuits. (C1 must be discharged).

Take time in desoldering the mosfet and the capacitor and keep everything clean. Make sure that you maintain insulation between the mosfet and the chassis of the powersupply.

Look at the warnings in the comments and answer. When testing the unit after replacing the mosfet, capacitor and diodes "Keep your fingers away" and do not to kill yourself.

If you are carefull and able to work clean the job can be simple. However if the parts blow after the first attempt then leave it alone and look for professional assistance.