Although the Twins are pretty much hamstrung and stuck with Joe Mauer for the foreseeable future, that doesn't mean there aren't some moves they could make to try to rebuild quickly - which they'll have to do in order to become contenders again before Mauer is completely out of his prime assuming he isn't already. Obviously the #1 priority should be the draft, where the Twins have the 2nd overall pick and three picks in the top 40. I'd like to see them concentrate on high upside, college pitchers who won't have to spend 4-5 years in the minors, and I'd specifically like to see them draft Mark Appel out of Stanford or Kevin Gausman out of LSU with that #2 overall, then look at more pitching with picks 32 and 42. Pitching-Pitching-Pitching.
Beyond that, there are some trades that need to be made. Namely:
1. Justin Morneau. Contenders like the Marlins (who just sent Gaby Sanchez to the minors), Dodgers (who have crappy no power James Loney), Rangers (great offense with wasteland at 1B) and Blue Jays (who have given up on Adam Lind) all could use the power Morneau would provide at first base and all have the money to handle his contract, if they aren't too wary of his health issues. Health issues and the big contract might mean his selling price is down, but a package of 3-4 players centered around one high upside prospect at a position of need would be a good move. The Marlins have 3B Matt Dominguez in AAA and although he's not a great hitter he's supposed to be a plus fielder and let's face it, the Twins are pretty much out of 3B options. The Rangers are loaded, including the minors, and that might make them willing to move future stud starting pitcher Martin Perez, who would give the Twins their first ace type pitcher since Johan. The Dodgers system is loaded with starting pitching (with 8 of their top 10 prospects starters), and the Jays have enough young pitching that they could part with a semi-highly regarded pitching prospect or three without hurting their long term outlook. Morneau is a great trade chip as long as he keeps hitting with power, and he's not going to be around by the time this time turns itself around - they need to use him to get the turnaround started.
2. Denard Span. I like Span and he's a quality leadoff hitter, but Ben Revere is a very similar player with less power, less discipline, and better defense, and the former two can develop with more time - time he's not getting. The Nationals have been sniffing after Span for a couple of years now and were even willing, or close to willing, to give up a real young, real good reliever in Drew Storen last year. I don't know that you can get a blue-chipper like that anymore, but the Nats are contending and are sorely lacking in the leadoff hitter department so they'd still probably love to have Span. With all their young pitching maybe you can get a MLB ready, middle of the rotation type guy who is still young like Ross Detwiler. Given Ramos's injury they need a catcher, so maybe throw-in Doumit and get a prospect back or even whichever second basemen they hate less, Steve Lombardozzi or Danny Espinosa - either would be a better 2b of the future than anything the Twins have right now.
3. Carl Pavano. I'd say trade the entire rotation, but I can't really see a team parting with anything other than "cash considerations" for anybody other than Pavano or Liriano, and trading Frankie when his value is at an all time low is probably not the right idea, so that leaves Pavano. He's not exciting, but he's consistent, a decent big league pitcher, and somebody (or multiple somebodies) are going to be looking for that around the trade deadline (not to mention he's affordable). All four AL East contenders have worse than average rotations so as that divisional chase heats up they're all going to be trying to outbid each other for pitching help, so depending on who else would be on the block Pavano could be near the top of their wishlists (although I don't know if the Yankees would be willing to bring him back). He'd bring back less of a return than either Morneau or Span, but getting a mid-tier prospect or even a youngish player who is blocked on one of those teams would be worth looking into.
4. Matt Capps. I really don't know if anybody is stupid enough to "pull a Twins" and give up something of value for a shitty closer who has racked up saves in his career more out of opportunity than talent, but if anybody is willing to trade anything they should jump on it. Same with Glen Perkins or really any other pitcher on the entire team.
Pull all that off, and maybe you're looking at a future of:
C - Mauer
1B - Miguel Sano (I'm guessing this is where he eventually ends up) with Parmalee backing him up
2b - Lombardozzi or Espinosa with Plouffe backing up
3b - Dominguez/Travis Harrison
SS - Levi Michael/Brian Dozier
OF - Revere/Benson/Hicks/Rosario/Arcia/Kepler
with a rotation starting with Kyle Gibson, Appel/Gausman, and Detwiler with Baker/Diamond/Walters (if either of them is real)/other draft pick pitchers/Wimmers/Hudson Boyd/Madison Boer/Adrian Salcedo also in the mix and Deolis Guerra your top bullpen arm.
I dunno. And that's not even counting in any other prospects that come back in trade other than Dominguez and the Nats' guys, although even though Dominguez is a 3b which the team sorely needs I'd still take Martin Perez over him if they have that option.
And yeah, I realize I'm just playing fantasy baseball basically, but the team is in the shitter and going nowhere, and you have exactly four tradeable assets so trade them. None of them are going to be around when this team gets close to contending again, so trade them now while they have value. Anything. Just do something this year rather than sitting around with their thumbs up their asses like they did last year. This is what I'd try to do.