Joe, I would concur with my colleagues that there is no inherent reason to assume moisture or stringer problems on any mid-1980s Carver or any model number that ends in "7" or higher. Please take a look at some of the other threads we've done on this Carver forum over the past year, because there will be more detail about Carver construction and some of the historical issues with older boats (many of which were faced by all the other manufacturers, BTW)...
In a nutshell, a model number ending in "6" or below (such as my 2896) has a balsa cored hull and tacked-in stringers (meaning a lot of the wood is exposed. This has resulted in water intrusion issues from time to time and some of these boats are not desirable values. However a good marine surveyor can tell you whether or not a particular boat suffers from this malady, and as you can tell from the fact that I own a 2896 and used to own a 2895 before that, that some of us aren't too worried about it. I've seen so many old Carvers I know what to look for and to avoid...
The 3607 is a newer design with a solid fiberglass hull, and stronger, thicker stringers. It wouldn't surprise me if there was still the potential for water getting into those stringers, because the construction techniques didn't change THAT much, but again a good surveyor should find this problem if it exists. The hull, being solid fiberglass on these models, is NEVER a problem unless you find blisters (which are generally fixable)...
I'd own a 3607 or 3697 now if I had the money...