I have a problem with the PC not coming on. Would a fan heater plugged into the same multiplug socket cause a problem with the power supply failing?

 

Only if the added current draw was enough to trip the breaker for that circuit. Have you checked that the heater also doesn't work?

 

Beenthere is right. If the heater is shorted or draws more current the power supply can provide, the power supply shuts down. Otherwise, the power supply has blown. Also, check the fuse of the cable connecting the power supply with the outlet.