I believe I first saw them mentioned on the unofficial Offspring forums, but everyone was trash talking them. The usual stupid critisisms, boring, cant write songs, LaBrie sounds like a girl. Unfortunately I based my opinion around that, and moved on. The more I got into metal the more I saw their name pop up, but it wasn't until I was getting into Symphony X that I heard my first Dream Theater song: Surrounded. On a review for Twilight in Olympus, the reviewer mentioned the striking similarities in the opening to Through the Looking Glass to Surrounded, so I checked out the DT song. I guess it was ok, so I put it on a mix CD. I wasn't sure about the vocals, but the song was growing on me. The next time I went to the local CD store I asked about DT and was recommended Live at Budokan. I was quite shocked when I looked at the track list as every song was like over ten minutes long. The only song I remember actually catching my attention was The Test That Stumped Them All, but I ended up trading it back.
I was already downloading music, but discovered some new and awesome websites where I could download full albums! Rhapsody would be the first victim (still haven't listened to any, this was in 2006), but then I found a torrent of Images and Words. Unfortunately the first track was corrupt, noted in the description, but it was cool, I just faded out the cut off. Images and Words became my favorite new album. I played the hell out of it. Then I discovered DT.net and learned that Pull Me Under is supposed to stop suddenly. I didn't ask, a bunch of people already had. But I didn't own the album yet, so I just continued listening to the faded out version. Soon I bought my first DT album, Scenes from a Memory (technically second if you count LaB), got IAW for Christmas and the rest of their discography over the next year, including Live at Budokan again.