Thanks for the search tips.
Unfortunately, any hint of the melody left me many years ago. It was probably all in a major scale, which would explain why I remember it as a happy song.
I've listened to the "island" songs here before, but I can at least say that
rainbow_island.xm has a similar level of complexity to the one I'm looking for. It's kind of like something you would hear on a snes or genesis game, but with a different soundfont. There wasn't any percussion, which added to the softness of the track. The tempo was probably around the same as the rainbow_island one, but could have been half that. The length was relatively short, probably no more than a minute or two.
I'm pretty sure I renamed the file immediately after downloading it, so any memories I have of the name could just be me remembering what I renamed it to.
There was no intro or fade out or much else besides the meat of the song. If I found it I think I would recognize it in the first 5 seconds.
This tune is similar to the style/intensity(?) I'm looking for, but that example is way too somber, and the tempo maybe a little too slow, and the melody doesn't stand out enough.