I had a similar experience a couple of years ago, upon beating Sonic 2 for the first game. More than any other, that game defined my childhood - like you, I would often go round to a friend's (or in my case, cousin's) house and spend ages playing it. When I finally got my own copy of the game, I passed whole evenings sat in front of the TV guiding Sonic and Tails through the numerous Zones. I remember getting as far as the final boss several times, only to have Dr Robotnik's bad-ass mech crush me right at the end. A couple of years ago I picked the game back up thanks to the Sonic Mega Collection Plus for PS2, and (with a bit of cheaty help from the save state feature) managed to finally beat it and see the credits roll. As you found with Sonic 1, the in-game pay-off was pretty anti-climactic, but the thrill of finally accomplishing what I never could all those years ago was immense.
Anywho, congratulations on your personal gaming achievement. Doubly so on nabbing all those Chaos Emeralds - that's something I'd never have the patience to pull off!