Remember back in the 80’s when those little electronic keyboards were all the rage? Most had some little song built in as a sample. If you were to use one of them as the basis of a song, would you have to pay royalties?
Technically yes, but I would check who the manufacturer is, they might be out of business, unless its Casio.
Personally I think you are safe, because who the hell will recognize the melody?
I sample things, and if I get sued that’s fine, it means I’m making money and being noticed. 
Once you’re sued, you won’t be making money.
Depends.
Jay Z has been sued a bunch of times, and he’s doing pretty well last time I checked.
I would imagine they go after people with deep pockets.
If you have deep pockets, you’ve already won.
I don’t know, but I hear the “percussion loops” from the Casio SK-1 in songs quite a bit these days. Not that I can think of any off-hand.
You could alter a few notes and be in the clear. When you say ‘basis’, how much of a basis do you mean?
I vaguely remember the hip hop producer Swizz Beats was sued for using one of those pre-programmed Casio loops. I don’t know how the case ended up. I just took it as confirmation of Swizz’s staggering laziness and unoriginality.
There was tiny Casio keyboard (maybe 20 keys) that had a 2-3 minute song. Let’s say I wanted to add other instruments and lyrics to that song.
What do you intend to do with it?
Release it commercially or listen to it while you go jogging?
For the sake of argument, I would want to release it commercially.
Also, let’s say I reproduce the song using different instruments as opposed to using the actual recording.
Any difference?
Well for the sake of argument then, you would most likely have to pay royalties or risk being sued. The melody is what is familiar so I could play “light my fire” on a harmonica, and I would be at risk I suppose.
I don’t really know the legal ramifications to be honest, but I do know making a sample the basis of a song is not the brightest idea.