Usually, if you need to ask, it is not a good idea.
That might be a gross oversimplification, but given what is at stake here (especially when US courts are involved), you rather want to err on the safe side.
Generally speaking, there are laws about how much art and deisgn needs to differ from other works to be seen as non-dervative... yes, given you change some things about the screenshot and make sure nobody can any longer claim with certainity that you started with a screenshot of the sims, you MIGHT get away with it.
But: you still can be sued, even if the court would likely decide in your favour... given that again US courts are involved, that means you will need lots of money just to defend your case. IDK if and what sum you get back if you win the case. And lets not imagine how much you are going to pay if you loose.
Clearly, the easy way out is just to avoid this whole mess and come up with original art. Will that art be as good as what you could have kitbashed together with sims screenshots? Most probably not. Does that really matter? Most probably not.
Just give it your best shot, or see if you can find an artists that is ready to work with you even in your financial situation.
It is better to have suboptimal art in your game than getting sued because of copyright infringement, really....
About your ad absurdum: yes, actually they could do that, depending on the EULA of the game. If you are not allowed to use parts (notes, building blocks in a voxel game, whatever) for commercial purposes, then the owner of these parts can by definition sue you if you compose anything out of these parts and try to sell it.
Again, given you run it through enough filters to hide its origin, Nintendo might have a hard time proving you did infringe the EULA, but then again you could have used practically any software at that point to compose the original melody before running it through the filters. And there is awesome software out there that doesn't cost more than Mario Paint, can record a melody and DOES allow you to use your work commercially afterwards.
That is also why many software companies, as well as content creators give you 2 license types to choose from today... a personal one for strictly personal use (so hoobyists can compose a tune for their holiday movie shown to their closest friends), and a more expensive commercial on for use in products that will be sold commercially afterwards.