Don't trust everything you read, there are a lot of cons online including fake emulators 3DS included that let you download a prog that to get to the full download forces you through several adverts generating money for that site to get a program that does not do what it states, homebrew runners are not the same as retail game running and may not have anything to do the real console, or simulate a small part that is used for things like homebrew testing.
Nintendo will repair the 3DS even if you did get it second hand you do not need to prove how you got it (this is not what you started out saying mind) you will be charged for the repair but it will get repaired for less than it would cost to buy a 3DS, no harm in asking them, as you may be able to get a working 2nd hand 3DS for less (can't see it happening though)