I don't have a photo unfortunately. Otherwise this would be simple .
A board that matches the specs and also has the exact same issue of outputting display only to an external monitor? I'm doubtful, haha.
That's an interesting idea about the logic board sticker. I was hoping there would be a database somewhere that would spit out some meaningful info with respect to that serial number, but there doesn't seem to be such a service. I don't know if Apple would care enough to weigh in, but it's probably worth a shot.
Few things you could actually look for. Assuming it's a unibody MacBook, the serial number should be printed somewhere (check around the RAM slots). I'm sure this is applicable to older MacBook's but I just don't know where to look. Second, check the serial number once you're in OS X through "About This Mac". This won't necessarily prove anything as the scammer, if clever, could've had a logic board with a blank serial number and then flashed it with yours but I doubt it because a few things would have had to happen. So your best bet is to check the logic board for your serial number - that's something they couldn't change, IIRC, it's not a sticker of your serial number, it's actually printed.