What IC use this inverter?Which transistors is there?How many?It's much easy to fix SMPS then make it,becouse You are sure it was work properly somethimes.You must check allmost all semiconductors.Start with switch transistors,diode rectifier...The hardest part is IC,but in most case death IC is overheating quickly when You turn on supply.I don't know how much You know about electronics but i will recommend You to desolder all parts before start measure with multimeter.That is best way to be sure in showing results.Use internet to search for datasheet about transistors becouse You must know wich type it is,MOSFET,bipolar,FET....You probably know it's not same principle to test it.
I think for start You don't have to remove diodes,becouse dead diodes act like short-connections in both way,so You can test it on PCB.In one way conduct in other have to show big resist.If show resist but not to big,it's probably OK but current flow trough something else on the board.If You want to be sure,You must remove it from the board.
If You find something dead-don't replace it and turn on supply immediately,search for more dead parts becouse You can "kill" again new parts if there is something else what You have to replace.
I can't type anymore.((@ Do You find something interesting in this post or You allready know all this?:afro: Start with testing semiconductors.