Starr > Favre and Rodgers in Packer QB hierarchy, so far, although Rodgers may have an outside chance to meet or exceed Starr's accomplishments. As has been convincingly pointed out by PackAttack12, all Rodgers may have been lacking over the years has been a reliable defense pulling their own weight. Lombardi (both the coach and GM) and Phil Bengston gave that to the Packers, as did Jack Vianisi. As has been noted earlier, blame the recent failures on whomever you want.
It was a privilege to see Starr in action. What's more, he dominated at a time when it was legal to hit the QB, head-shots included, even fairly long after the throw had been made (when compared to the rules being enforced today). And the DBs could pretty much make contact with the WRs all the way down the field, not to mention that O-linemen protecting him could not legally hold back in those days. He called his own plays, too. The passing game was not so heavily favored by the rules in those days as it blatantly is today -- not like the Arena League Lite (NFL) throw-arounds commonplace to the game of today.
Despite the disadvantages of playing QB back then, Starr also earned five championship rings, same as Brady. To me, Starr's five championships were harder-earned and, thus, even more impressive. That puts him at the top of my all-time GOAT list. Starr, Lombardi & Company accomplished their totals in far less years total than it has taken Brady and Belechick to do the same thing. It doesn't diminish the accomplishments of the latter, just adds a little perspective to their records.
Otto Graham also deserves some serious props for his own impressive number of championship game appearances and his seven championships total, although some of those were earned playing in a league that arguably had much lesser overall talent to oppose him than what was found in the NFL even back then. But he won four in the NFL, too, so he deserves a prominent place in NFL lore -- behind only Starr by a whisker or two and arguably followed somewhat closely by a very small handful of others. Take your pick.
Some of you think that Rodgers has been slighted? Just take a look at ESPN's obituary for Otto Graham:
http://www.espn.com/classic/obit/s/2003/1217/1688946.html
ESPN mentions all-time QB greats, including Namath of all people, but not even the slightest mention of Starr and his championships in this article naming the GOATs. Rather like a lot of Packer fans still overlook today.
For what it's worth, IMHO Bart Starr is the GOAT at QB for the Packers and arguably for the entire NFL, as well. That's my story and I'm sticking to it. Rodgers probably is destined to be #2, at worst, and can still make the ultimate climb if this team ever assembles a consistently good enough defense over the course of the next several seasons.