You need to understand us.
I'm happy to believe the internet was slow and unreliable back them especially from the countryside (actually, I know it for a fact), but assuming a 7 hour night and a 1 second wav file (176.4 * 1000 * 8 = 1411200 bits, I made a mistake in my last comment) would mean 56 bits per second, that's 7 bytes/sec, that would be unusable to browse the web, even by the standards of this past. That's also far from what a 14.4 kbit/s modem is supposed to achieve, even considering that 14.4 kbit/s is a theoretical max and you'd be typically way below this speed in actual use. Hence our surprise.
At this speed, it would have taken you several minutes (and since the internet was unreliable, probably several attempts) to even load nintendo.com and then the download page. The simplest page I know in the wild, perdu.com, is 203 bytes, 909 bytes with the HTTP headers, that would take more than 2 minutes to load at that speed. nintendo.com was likely more complex than that. Given this, you'd have to have some very strong will and patience to go ahead and download a sound for fun as a child (though I can picture this).
I can only assume it didn't take the full night (you woke up on a finished download, it most likely did finish (way) before you were done sleeping), and that there's more to the story that the elements we have. What's still strange to me is that if it took say half an hour, with such a strong determination, would you have gone to sleep instead of excitedly waiting for the download to finish?
I'm not saying your memory is wrong or that you are lying or something like this, I'm sure this recollection is genuine and that it is a strong and fond memory, and I understand that it was long ago so difficult to remember the details, just that we are missing some critical piece to make something complete of your story for ourselves.
And sure, not everything can be reduced to math, but that's our best tool for estimating / evaluating stuff as distant observers.