Second one that stands out to me is Muse - Plug In Baby. First time I heard this, they are playing a festival that was being shown live on TV. Can't remember what one, but it made enough of an impact that I got up the old 56k modem later that night (it was a while back!) and looked them up..
And then ended up buying a bunch of their albums.
https://youtu.be/dbB-mICjkQM
Last one, which is more recent and a little different. I was watching Luke Cage and there was a nightclub scene with (as I remember) an act doing a warmup, or audition or something. Loved the song and, thankfully this was recent so it was easy to look up online, turned out to be Jidenna - Long Live the Chief
https://youtu.be/H_AQFnqMY3E
Reason I say it's a little different is it feels like I came across it less 'organically', being introduced via a TV show. Granted, the Morcheeba and Simon & Garfunkel one were marketing exercises also, but in a different way - they were used to create a particular atmosphere/ambience, whereas the Jidenna/Luke Cage thing felt more like a product placement. Out of all those stories, that's the one where I only really ended up liking the one track rather than getting into the artist generally.
The 'least cool' band I got into story has to be the Simon & Garfunkel one, though. I was a teenager at the time, on holiday in Newquay, UK, and I was sitting in some restaurant. They stayed playing a bunch of what I later found out were Simon & Garfunkel songs. I asked my dad if he knew who it was, he told me, but damn, I was getting condescension vibes there.
Anyway, bought their greatest hits album shortly after.
https://youtu.be/DdIC4ZXVq9k