I'm a little unclear on the details of the problem, but does the system work 100% fine with the old battery (hopefully you have it around to test)? If so, the new battery is the problem. I'd definitely try a different battery before proceeding.
When you remove the battery, is the AC adapter light bright green, and does it power the machine? If so, I wouldn't really suspect the AC. I've never seen an AC that worked fine, yet was responsible for a battery not charging. It's worth trying another, but it's not likely the problem.
Does the "green light barely visible" situation only occur when a battery is connected? I'd suspect your DC-in...either that or the internal battery connector, and if neither of those, then the logic board itself. Sellers often state that their DC-in boards are tested and working, but realistically they are difficult to test, and most sellers don't bother and just cross their fingers.