For me, it comes down to this:
Do the Rangers, as constructed, have what it takes to win the cup (i.e. win four 7-game series against the other top teams in the league)?
In short, no.
Why?
First and foremost, due to the lack of a true, dynamic, first-line center. There's no one on the roster who fits the bill and no one in the system who is likely to become that player - the center prospects the team controls simply don't have that upside, much as I like guys like Lindberg.
Therefore, they should do what is necessary to acquire that player. And, conversely, avoid all moves that would make acquiring that player more difficult.
Signing Girardi and Callahan makes acquiring that player more difficult, because propping up this current roster such that it's 2-round worthy makes it that much more unlikely that the Rangers will be in position to draft such a player. Letting them walk makes acquiring that player more difficult, because such players NEVER hit UFA, so the cap space freed does not help. Therefore, you MUST trade them, either for kids who have a chance to become that player or for draft picks that you can use to find that player.
Get on it, Slats.