Give it a go. It is a lot easier than you think. What have you got to lose?
Mine’s a 7-8 y.o. 40″ 40EM something or other. 13 screws hold the back cover on. The first thing you see in the middle is the PSU. 8 screws remove that. Flip it over, the blown cap(s) will have a swollen appearance to the top. Flip back over and de-solder. You will find identifying marks. Google / eBay these. For Evans sake, your local Maplin will probably have them (mine did, and a helpful chap who knew what I was going to use them for. This fix really is that common!)
Get them thar caps home. You will notice the legs are longer than the one(s) you removed. This is a good thing. Slide the legs into the holes in the PSU board, make sure to observe polarity. For my Samsung there is a ring printed on the circuit board (really normal, helps assembly ops) There is a thick edge to one side of the ring. This corresponds to the polarity stripe on the capacitor. If in doubt compare to other caps installed on the board. Bend the legs – now that extra length makes sense. Solder the cap into place and trim the excess legs.
Refitting is the reversal of removal.