I have no idea how to decode the year directly from the ser. #, but I think there is a date-stamped metal plate somewhere on the thing with a date on it. Try looking on the engine block, the firewall, and the frame rails under the hood for a start.
It can't be too old, since NH hasn't had a TC45S on the market for very long; certainly not much more than 5 years, if that long.
The year really doesn't matter anyway... what is more important is the number of hours on the meter. If it's less than 300hrs, it's nearly new. If its not much more than that, and it's just starting to be broke in.
I'm pretty sure that the S is 'Supersteer' which means you've got yourself a very nice little machine there. It'll turn a real tight circle, way tighter than you would expect for a tractor if it has Supersteer. Go slow doing it though...
As for the mower, you probably have a sheared pin, or you haven't fully attached the PTO shaft to the tractor. It should have a ring on it that will snap in good and tight to the tractor when it's on correctly.
The other possibility (unlikely) is that the gearbox on the mower itself has been pulverized internally and needs to be rebuilt. It should have an oil drain on it, you can open it up . If you smell burned oil, or if you see a lot of metal in the oil, that's your problem. I doubt that is the case, those gearboxes are pretty tough and can take a real beating.
Go see a dealer to get a new shear pin, or you can get them at any Tractor Supply Co (TSC). You might think about putting a slip clutch on the mower to remove the possibiliity of shearing another pin once you get it running. They do their job, but replacing them can be a big pain in the butt when they shear off at the far end of a field.
