The DS lite power switch is known to be quite unreliable in the longer term, though it is usually it not working that is the trouble and if not abuse then a lot of use. The same thing that saw the switch fail open could see it fail closed but it would be super rare.
I have seen this for other electronics, though it is usually someone like mechanics and grinding types that end up with conductive dust going into their phones and tools that sees connections short out where this sounds like it is not that and not even close (not to mention the DS lite switch is fairly self contained).
If it is random then you are going to need some fairly specific gear to test things, or you can fire the parts cannon as it were and replace the switch*. If it constantly happened then that would be another thing. Also before touching the soldering iron to the board check there are no other reasons for it to conduct (dust, some insects, rodent urine/rodents themselves which is not really a problem for this but remember it for larger stuff in the future).
*technically you could remove the switch and see it is some other errant signal that is causing this but eh.
Do also check you have not got a funny sibling that likes to turn things on, move them just a bit or the like to mess with your head.
