I'll echo Jensen's comments about making sure the mains connection is DISCONNECTED before even removing the cover to start looking at this fix. The potential for shock after that is very small, and in my experience, the size of capacitors in these power supplies aren't enough to give you even a small shock, but as he says, shorting something to anther component could easily blow something else. Transistors and Integrated circuits don't handle sudden power surges well. That said, this is a very easy fix, as again he says, which should be a very simple procedure.
I'm a bit pressed for time until the weekend, where I hope to get the box off the shelf, and strip it to take pictures and do a proper tutorial, but here's a basic tutorial:
1: REMOVE THE MAINS POWER FROM THE BOX !!!!!!
2: Remove the 5 screws that hold the metal lid on the box, and slide it to the rear to remove it.
3: If your box has an internal hard drive (I can't imagine many don't?), remove the screws and the SATA/power cable, from the drive, and lift it out of its cradle. Put it to one side.
4: The ribbon cable that connects the power supply to other components is underneath it. Gently press on the tab on the side of the connector strip to unplug it (you might need to get a flat edged screwdriver to prise the tab on the side of the connector to allow the plug to be removed, be gentle). DO NOT try to remove the end that is connected to the pcb (printed circuit board) of the power supply itself, it is fixed, and permanent. If you break that end, you'll have a lot of soldering to do to rectify it.
5: Unplug the "molex" connector that feeds the hard drive.
6: Unplug the small two pin connector which is the mains power supply to the pcb.
7: Unscrew the four screws (one at each corner) that hold the pcb onto the chassis of the box.
8: Jiggle the board out of the box, so you have it free in your hand. (Not strictly necessary, but removing and soldering components in place can be tricky, this makes it easy).
9: Locate the capacitors mentioned in this thread, and identify where they are soldered to the pcb. In my case, only one capacitor had bulged, so it was easy as it's close to the edge of the board.
10: Remove the capacitor/s ( TAKE NOTE OF THE POLARITY OF THE CAPACITOR AS YOU REMOVE IT). The Capacitors have markings identifying positive and negative terminals. Usually on capacitors, it is the negative (-ve). Again, usually it is a stripe on the side of the capacitor with a "-" or -ve" marking on it. Use a soldering iron of a low wattage, and de-soldering tape, or a "solder sucker". If you're lazy like me, or can't find your solder sucker, simply apply the soldering iron to on side of the capacitor and as the solder melts, apply pressure to pull the connection through the board. Do the same to the other side, and don't worry if you don't get it in one go, simply do one side and then the other to stagger it out. Once the capacitor is off the board, use the soldering iron to clean the solder away from the connection so you can see the hole which you will have to put the legs of the new capacitor though. If the hole is blocked with solder, you won't be able to get the legs back through the board to position it.
10: Once you have replaced the capacitor with the new one, apply the soldering iron, and solder it back to the board. If, like me you have used a higher voltage version of the capacitor, you will probably need to "jiggle" it to make sure it doesn't put pressure on the components surrounding it, as the capacitor will be slightly larger than the original. It's ok if it touches other components, and won't short out that way, but for air flow and thermal reasons, leave a gap. There's plenty of room.
11: Replace the power supply pcb board back in the chassis, connect all the relevant cables/plugs from it and the hard drive, and put the lid of the lx3 back on.
12: Connect all the relevant leads HDMI/ethernet/dish connections etc. The last connection you should make, is putting the mains cable back into the box. Power it up.
13: The box should show the normal booting/loading/percentage....etc etc, that it usually does, and load up.
14: Put the kettle on/crack a beer.
15: Enjoy