No one is going to give away a QB to suddenly make it all better. Why would they? What level of overpayment would the buying team have to pay in order to ply even a mid-level QB away from a team. What does that do to cap management?
At best, you're going to get an underperformer, which they have now, so far anyway. At worst, you're going to overpay for damaged goods or a locker room cancer, one that the selling team is happy to be rid of.
Guys, there's no quick quick fix. It takes years to build a team to win. The foundation for the 2001 team was already here with Vinateri, Bruschi, Law, McGinest and Milloy, and they all lost the super bowl in 1996. It took that 2001 FA class of Terrell Buckley, Mike Compton, Bryan Cox, Marc Edwards, Larry Izzo, David Patten, Roman Phifer, Anthony Pleasant, Antowain Smith, and Mike Vrabel to come in and bring new blood to the team. Oh, and they found a QB on the bench, too, plus drafted Richard Seymour and Matt Light.
You wanna know how to build a team? There's your roadmap, right there. That part of the game has not changed. Bring in 2-3 top tier OL, a bonafide WR that stresses defenses, a top QB that doesn't give the ball away, a true 3rd down back, all while keeping this defensive core together and get it all under the cap. That's how many players they are away. Never mind the top two defenders just went down with maybe season ending injuries. No big deal, next man up.