But what you're describing is a property law exercise from law school. Basically, you are hoping for an easement, which can be established in a few ways, but you will have to dig up some background facts behind the servient property (your property) like - were the two parcels once joined together? how long did the adjacent landowner allow access through the dominant property? did the servient property owner make any substantial improvements to the servient property? how open was the servient property owner's use of the access route through the dominant property? how open were the improvements to the servient property? I just looked and Wikipedia does a good job of laying out the common law on it. But it's not NH specific, of course.