Value is very location dependent, so you need to see what they go for in your area. However, you would expect the engine is only a core for rebuilding and it needs a rear end. You want to look closely at the frame, especially on a convertible because they tend to have more issues with water infiltration. The vertical headlight Galaxies are 65 - 67. 65 and 66 look very similar, but 67 is completely different sheet metal. FE's are expensive engines to build/rebuild and body panels can be tough to come by, but mechanical stuff should be readily available.

The real question is what do you want to do with it? I'm sure it will never be worth what you put into it, and probably by a long shot, so how much can you do yourself and where do you want to start from. If you have to put $10 - 20 K into it, how much do you want to pay to get on that ride?

also, do you know what rear axles would be compatible with a galaxy? will a fairlane or a falcon axle bolt up? or even a mustang rear end? just wondering what i would need to look for

I admire your ambition, but would agree that a salvage yard find may not be the best way to go for a first project.

My car came from central Illinois and was purchased for $7500. In that part of the country classic cars are cheaper. The '65 I'm referring to is a 500xl has the original engine, rear , and trans after checking all of the numbers, still has the original interior, and has 44,000 documented miles.

You could easily have three times that in the car you're talking about. I'm only using mine as a reference to show that if you're patient, the deals are out there. I would gladly put you in touch with my friend who found this car as he ALWAYS seems to find solid old Ford products. He found my '68 Cougar, as well as this Galaxie and he also restores/builds cars for people.

Whatever your decision, be objective and realistic about what your looking at. If I find anything here in Georgia, I will be glad to give you a heads up. But be prepared to pay more in this part of the country. The same '65that sold for $7500 back home would be more like $10-$13000 here in Atlanta.

Good luck with your search. As far as what will fit, I wouldn't bother with a Mustang, Fairlane, or Falcon. All three are much smaller cars, and a lot of them cam with the 8" rear end, which in a small block mustang, etc. would be fine, but those cars if they came with a big block used the 9" rear for a reason: Strength. To the untrained eye it is easy to mistake an 8" rear for a 9" rear as they both load the differential from the front. Also, just going by my '68 Cougar which uses many Mustang parts, the car is much more narrow. I will be glad to give you a measurement from my '65. 

Also keep in consideration the following:The Mustang/Falcon rears are leaf spring rears, while the '65 on were coil sprung three link rear ends so you would also have issues with mocking up and welding the correct spring perches etc. So with that make sure the other pieces of the rear suspension are there with the car. Otherwise you will be searching for the other components as well.

I'm not trying to discourage you. I'm just trying to give you a heads up on some other things to take into consideration before you pull the trigger. You might try looking for a decent roller (car that at least has the rear end) for a first project. Or even one that is complete but needs work. 

I agree with 70XL. I wouldn't mess around with the VIN's. You could find yourself if some real trouble if you ever got caught. Just for your information, there could be stampings of the VIN in other locations on that car. For example when I was cleaning up the frame on my 61, I discovered a VIN stamping on the top of the frame rail on the passenger side just in front of the the firewall...who knew?