Another ring? Whats his first one? His wedding ring?
You are right.

Oops, my bad.
He's been around for so long I thought he had at least one. Anyway his career stats are impressive, he's done a good job, but now he's old and in decline and it's a good year to retire. In that age range of 34, maybe 35-ish is usually a good time for most NFL QBs to leave the sport if not earlier.
Any older, then it usually shows that he is no longer the same player and should retire. This is when fans start pleading with the player to hang it up. Outside of kickers, I can't think of many players who should play into their mid-30s and smart teams should always be bringing up new talent. Keeping an eye on the future is what keeps a team good year after year and mostly in the W column for more than a decade.
I think if he had a chance at an SB ring, it had already passed. The only thing he can do is to add numbers to his impressive stats, but like Favre would probably add numbers to his likely hall of fame induction but not realistically help any team in the process. At this point, and for at least five years, Favre has been adding numbers to his stats but not with what appeared to be the intention of helping the team or coach he was working with. One can almost sense the ego taking over. His earlier, more productive years in Green Bay where he went to two Super Bowls was when he was much more of a team player. That mid-90s Packers team was a well oiled machine with other strong weapons besides Favre. This kept him humble.
Warner did the classy thing and retired as did other great players like Barry Sanders who left while he was still great, but no longer on the rise. It's best to quit while one is ahead, and preferably after winning a Super Bowl, if possible.
For instance, if I were Brady or Peyton Manning and I won the Super Bowl this year or next, I would find it a great time to exit the NFL. Brady would have 4 rings and 5 SB appearances, and Manning would have 2 rings and 3 appearances and passing numbers unseen by any QB outside of Favre in the NFL right now.
Who wants to see a 40 year old Manning or Brady out there? And what shape will those teams be in when those two are starters into their late-30s or 40 and then retire? A new team would have to develop around a new QB and those teams would be in the NFL doghouse for five to ten years. This is what happened to the 49ers after the long run of Montana and Young and what seemed like a default winner every season, until it wasn't and then the team was put into a rebuilding phase.
Hopefully, if a team plays it right, at worst a rebuilding phase should not be any less than an 8-8 season.
What can make the Patriots or Colts have a two decade type of dominance in the NFL like the old school Cowboys is if 1) they have a good backup set of coaches first and foremost, and then, 2) groom a QB as good if not better than a Brady/Manning. When SF had Montana, his rating numbers were through the ceiling and when Young took over as starter, not only did he match Montana's ratings, he surpassed them. This is what the Patriots and Colts have to shoot for and there is still time to look to the future while maintaining winning teams. Indy will probably have an OK season and the Patriots, if they never win one more, have had a great season.
As for other classy exits were the Bus from the Steelers after his Super Bowl win and Elway after his second Super Bowl win. Yes, there were some who wanted to see "one more", but as it turned out it was for the better to leave an ultimate winner.