The OBEY occured to me in two stages.
Stage 1:
I got a TurboGrafx-16 back around 2010 I think. Even at that time, TG16 game prices were getting to be very high. This limited what I got to play, which wasn't much. I liked Keith Courage, Victory Run, Dungeon Explorer and Bonk's Adventure, but this isn't what the TG16 really had to offer. I parted with the TG16 and thought I could live happily ever after with Neo Geo.
Stage 2:
Fast forward to 2015, I had experienced Neo Geo, it was good, but the OBEY guilt crept up on me. I righted my wrongs, I bought a white PCE, Turbo Everdrive, a Duo-R and a pack of CD-Rs. I've been very happy ever since. I hooked a friend up who was looking for PCE happiness with my Duo-R, I then proceeded to get a plain Duo which I have been greatly enjoying ever since fixing.
As for when I realized it was magical... Well, I had a faint feeling of it with the TG16, but it was fleeting. Once I had a real PC Engine and access to any game via Everdrive/CD-Rs, I was engulfed in the magic.
I think Ninja Spirit was the game that pushed me over. As good as Shinobi and Ninja Gaiden are, there was something awesome about Ninja Spirit that I hadn't found in a Ninja game before. I thought to myself, "this is Hudson Soft". As I played each Hudson Soft game, I kept wondering how they could possibly have made so many quality games. There must be some magic in that old 6502.
I feel ashamed for having ignored the PC Engine for so long, but I am definitely a fan now.