There may not be an official salary cap, but there is an unofficial one - salaries will always be capped by available revenue minus other expenses and a profit. Baseball is a business, and owners are there to make money, not lose money. The idea that just because the owners have money there is a moral obligation to let a business be an ongoing loss-maker is wishful thinking at best. New York and Los Angeles will always be able to spend more on salaries, because they will always have more revenue available to them, especially from local TV contracts.
That being said, I think this whole idea that money would solve the problem is also off-track. Having a high payroll does not guarantee success (Cubs, Twins last year), and having a low payroll is no guarantee of being a celler-dweller (Tampa Bay being the most notable example, but there are others). A good GM can field a competitive team, capable of winning the series, with a payroll of $95-100M, which is right about where the Twins payroll is, so I don't buy the argument that they are being held back by cheapskate owners.
Personally, I don't want to see Greinke or Hamels recruited by the Twins. Sure, I'd love to see them in a Twins uniform, but I think the money required to sign one Greinke or Hamels could be better spent on 2-3 other players, all of whom collectively could have a larger impact on the team than a marquis pitcher who plays once every 5 days. Do we use that money to fill one hole, or to fill several?
I agree there need to be some offseason moves, and acquiring some starting pitching is a major necessity, but I'd rather see a plethora of moves that fill multiple needs. That would say to me more clearly that the Twins are serious about improving than signing one big-name player.