Overly long/dramatic story below, but hey...
Even from about the age of 11 or so, I'd always wanted to hear something akin to prog metal--I wanted to hear an eleven-minute song with a two-minute guitar solo, five verses, and four choruses. But I never knew any such music existed, or that there was a term for it, so for much of my teenage years, I languished around listening to a lot of rap metal, alt metal, punk pop, etc. appreciating the hooks and what not but always finding it sorely lacking in...well, progginess, I suppose. When I was 16 I finally discovered the first album that got anywhere near what I wanted--Avenged Sevenfold's City of Evil, still my favorite album to this day (for nostalgic purposes if nothing else). That album was so far beyond anything else I'd ever heard that I listened to nothing but it (and the clean-vocal songs from their previous one) for basically the entirety of the calendar year 2006. By the end of that year I was faced with a dilemma--I'd burned myself out on the same 15 songs, but no other music I'd heard compared to them, so I couldn't derive enjoyment from anything else either. Avenged Sevenfold also kind of defies characterization--back then they were often called a "metalcore" band with "emo" elements, but I knew of many other emo bands and many other metalcore bands, and none of them sounded anything like City of Evil, so it's not like I could just go find other bands in their genre and get what I wanted.
So in early 2007, I started just downloading a bunch of stuff on whims, trying to find something that clicked. Since, at the time, the biggest thing I wanted to hear was guitar solos, one of these whims was checking out the Guitar World Top 100 Guitar Solos list. So I get all this music on my iPod, and I took to listening to it on shuffle for awhile, hoping that something would come on and grab me. One morning at 6:30 or so, I'm having my normal half-asleep walk to the bus stop when a song pops up that I had never heard of, by a band I'd never heard of. It sounded interesting--very retro, but still clearly better-produced than classic rock stuff. I figured it was something from the Guitar World list--which it was, at #98--so I'm listening to this song, and it sounds interesting enough, clean vocals, some interesting rhythms and riffs, but I'm waiting for the solo, hoping it's something actually interesting and not like some of the other solos on that list, which are iconic but completely basic (Smells Like Teen Spirit, for example). The solo finally comes, and it's a minute-long facemelter. I thought "Okay, maybe this is what I've been looking for." The song was Under A Glass Moon.
So I spend the day listening to this song between my classes and such, waiting to go home and figure out who this Dream Theater band is, what this style is called, when the hell music like this was made. So I got home and looked them up on iTunes, and I'm like "Hmm...1992...but they're still around now...eight albums, very cool...progressive metal, eh? Alright...WAIT THEY HAVE A 24-MINUTE SONG. THIS IS IT."
I didn't need to hear another note to know that Dream Theater was my favorite band. They have been ever since.