New guitar...why are the strings on the frets?

I came across a nice Tak dreadnought on the clearance pile at a local shop..
Solid top, excellent build, great price..
One problem...NO action, I don't mean low action, the strings are literally on the frets,.
I can't see any damage, there is plenty of saddle, the nut looks fine, the neck isn't popped at the joint. The strings have reasonable tension, and there is a bit of relief.
It's a nice guitar, and if this is simply a set up thing, (more relief?)it would be a find..what am I missing?

a warped or sunken top could be the problem if everything else seems ok ... google JLD Bridge Doctor which may help fix the problem without more radical surgery ...

That would make sense, perhaps the top was exposed to weight during shipping, ( nice guitar, but I don't believe it would have shipped with a case...)
Interesting link, probably not economically feasible in this case, but good to know its out there..

What model Takamine? I'm sort of a Tak nut.

Acoustic-electric Taks, at least the F-series models, have plastic shims under their saddles; perhaps someone took these out to lower the action, and lowered it too much. It's also possible that a shim or two came out unnoticed during a string change. You might wind up with a pretty nice instrument, just by experimenting with some thin, flat pieces of plastic. There's discussion of this process somewhere in the technical section archives at the Takamine Forum, link below.

http://www.takamineforum.com/

Another possibility would be to make a new bone saddle (saddles? are they the split kind?) deeper to compensate for the missing shims, but replacing the shims would be cheaper and easier.

It's one of the "tsunami" guitars , I haven't been back to look at it as I was under the impression that new ones were NLA. I see that is not the case..
It is actually for a friend who lived in Japan for a year, she had expressed interest in one and is on a grad student budget so I thought this might work for her.
I think it has some hidden damage ( maybe a cracked brace) that has allowed the top to sink just enough to cause problems , as the saddle is quite high. I always need to take those shims out of the Jasmines I buy for students, I think the high action is why there are so many around 2nd hand. lol.
Thanks for the ideas..

Humidity Damage?

That guitar probably has a severely overset neck angle. A 'sunken top' will not take a guitar this far out of 'correct' geometery...if the neck set angle was correct at one time. Go back ot the shop. Set the butt of the guitar down on the floow with good light hitting the fretboard. As you stand behind the headstock looking down the neck, judge the line of the neck. IF the guitar has a good line, then you are curious about the neck set angle. To judge this, imaginarily 'shoot' the line of the neck toward the bridge. IF the guitar has a radiused bridge, the line of the neck should hit the top of the bridge/bottom of the saddle from the G string over to the high E. IF the bridge is built like a 'classic' American bridge...that is, thicker on the bass side than on the treble, then the line o the neck on the bass side will shoot just a bit down into the wood of the bridge. IF the guitar has a 'flat' bridge with no radius as do Taylors and some Gibsons, then one must peek over the nut and jduge the line/angle of the G string. The line of the G string should hit the top of the bridge/bottom of the saddle. MInor/small deviations from a 'perfect' neck set can be acceptable, but these deviations limit set-ups. Slightly overset necks will not allow high action becuase the saddle will be too tall and thereby put excessive pressure on the saddle....adn soemtimes breakout of the saddle slot...breaking the bridge, right? Slightly underset necks can be set-up, but the gutiar might not ever be able to achieve a low action set-up.
ON this guitar you have looked at, Warm Guns, the line of the neck will shoot way up into the saddle. Yes, a 'sunken top' can contribute to this problem; but a top that has shrunken and 'dropped' will not take the geometry so far out of 'correct' that the strings will be on the frets.
Geometery is the first thing I look at on a guitar. IF the l ine of the neck and/or the neck set angle are not correct, I don't even care what the gutiar sounds like...because it will never play well or in tune. I have seen brand new D-45's that have had such underset neck angles that they were not worth putting strings on.
FWIW, learning how to read geometery is the most important aspect of understanding a guitar, imho. I have never palyed a new guitar that plays as well as it could, but the geometery tells me how the guitar can be set-up....or whether or not it can ever be set-up properly and make music. A few seconds of careful observation can sometimes save a person thousands of dollars and/or much trouble.