It's hard to give up on failed startups in cases where a lot of effort was involved and/or you still think your idea is quite clever/novel.
Perhaps people impressed with your successful startup might look at your previous attempts more seriously.
I think it's a symptom of small thinking for your current startup...the one that is succeeding. Why would you distract yourself and your customers and your media coverage from a winner and direct it all back towards a loser?
I'm not saying it's impossible to have left behind something worth pursuing. Maybe you did give up too soon, or maybe you had to choose an expedient path rather than pursuing something harder. I don't know. But, if you have caught a wave, now is not the time to try to scope out other waves. There are always new waves on the horizon, but you'll never get to shore if you don't ride one out.
Would many people have taken twitter seriously if its founders were unknowns?
You're asking us to know something that is impossible to know. But, I've met Evan, I've read the story of Blogger, and I've heard him talk four or five times about his history with all of his companies. I don't think I would ever bet against him, regardless of whether people take him seriously or not.
And, of course, Evan was finished with Blogger before he embarked on other things. Twitter wasn't an old company that he revived after selling Blogger to Google. It was something new. He tried other things along the way, and when they failed or didn't succeed the way he'd hoped, he moved past them and tried something new. He's practically a poster child for doing the opposite of what you're suggesting.
I would say a better option would be, if possible and compatible, to merge the technology, research and already done work from the previous one to the current one. I know this is not possible always, but if it is.