Hello.
Not all K codes were GTs. The GT package wasn't even available until mid April of 65, and Ford started selling K code Mustangs in June of 64. And, after April of 65, many of the K codes still weren't GTs. In order to tell if the car actually has the original motor, you're going to have to look at some things on the car. The cars vin will be stamped on the block right above the oil pan on the passenger side, up towards the front of the block. The balancer on the motor will be a lot thicker than the normal 289 balancer. It should be like an inch and 13/16 thick instead of slightly less than an inch. The heads will have date codes, but you have to pull the valve covers to see them. However, on the front outboard corner of the driver's side head and rear outboard corner of the passenger side head, there will be a two digit number. That number will be either 19, 20, or 21. If it's anything other than that, that isn't a K code head. The water pump will be aluminum, not cast iron. The fan will be much heavier, with some rivet type counterweights on it for balance, and will have the fomoco logo, SC, a date code and the engineering number of 911960 stamped on it. The alternator pulley will be 3 7/8 in diameter (and really heavy.
) and have the part number of C5AF-10344-C stamped on the face of it. There's a lot of stuff to look for.
The reason for all of this is very simple. You asked what the car would be worth. A decent set of K code heads will run you about 1200 bucks if the car doesn't have them. The fan will run you about a grand if you don't have it. The alternator pulley will only run you 3 or 4 hundred bucks, but it will take you at least a couple of years to find one. A decent set of 65 K code motor mounts runs something in the thousand dollar range also, if you can find a set. That Carter 3939S fuel pump is virtually unavailable. If you do manage to find one for sale, it's going to set you back at least a couple grand. Same with the correct manual choke Autolite 4100 carb. The one used on K code Mustangs was K code Mustang specific, and not used on anything else. They're reeeeeeeal expensive.
. If the car has all of the right stuff, you have a good find there. But, if all, or most of that stuff is missing, that's another story entirely. The car would still have value as a project, because it is a K code, assuming that it actually is a K code body, and not a car someone welded the fender aprons from a K code into. But, the value of the project would be considerably different if the car is missing $10,000 worth of stuff. Hope that helps.
I found a K-code coupe... 
