As for getting a replacement, RS components or Farnell are international companies with huge ranges of parts, if you can't find it at either of their sites then it doesn't exist. Well it's either that or their bizarre layouts got the better of you and you gave up looking, they are extremely confusing that way.
To de-solder an LED isn't that big of a job, it's only two pins after all. I recommend that if you do want to do it yourself, don't be fooled into thinking a low temperature is a good thing because it's not the temperature that's the problem, it's how long you apply the temperature, and if you go for 320 degrees C or something ridiculous then you'll have to apply that heat far longer than you'd have to apply 360 degrees. You might not damage the PCB and the LED doesn't matter as it's dead anyway (not sure how you broke an LED by dropping it, did one of the pins snap or something?), but PCB tracks are good thermal conductors and you might end up reflowing a different pin or otherwise damaging a component on the same tracks as the LED, but as I said, if you go for about 360 degrees you'll be fine.
Another thing I do when desoldering is to apply some fresh fluxed solder to the joint, this likely uses silver solder with no flux in it at all, meaning that it takes a long, long time to heat up enough (because it's silver) and doesn't flow even when it is heated (because it has no flux). Adding a small amount of fluxed lead-tin solder means you can heat it up much faster and it will all flow much more nicely, but really if you do this you should have some desolder braid on hand to mop up any solder left over from desoldering the LED because it's generally not a great idea to mix silver and lead solder, not because it's unsafe but more because they aren't really supposed to mix.
Finally, when it actually comes to desoldering the LED, you just heat one leg, apply force to pull it away from the board (you have to make sure the solder has melted before you apply said force, of course, and don't apply too much force), heat the other leg and apply force, and repeat. You might burn yourself a little but that's just part of the fun, and you will find it's difficult to begin with (because the LED is probably sitting flush on the surface of the PC with very little room to move) but once you get it going it'll come a lot faster.
I have no idea how hard this would be for a beginner with a cheap, cheap soldering iron, but if you're in the UK feel free to send me the board and replacement LED and I'll do it for you (for free) if you like. Trust me, I am a doctor.
.I just hate wasting £100 worth of sli-pro because of my soldering skills lol
