When getting the replacement screen, make sure that you make it explicitly clear that you need the 2nd gen screen, because $84 for a full screen assembly on the 2nd gen Moto X sounds way too low to be possible. I've spoken to all of my wholesale suppliers, and the lowest they can get screens for is about $220. That's glass, lcd, frame, and all connectors pre-installed. I understand CPR gets a bulk discount the likes of which us little guys can only dream, but I cannot imagine that they can get a $220 screen for $84. In fact, $84 sounds about right for the FIRST gen Moto X, so it's entirely possible that the person you spoke to just has no idea what they are talking about and is selling you the wrong part. Just an FYI. I'll also be putting up a full, step-by-step guide as soon as we get our shipment of screens in, probably in about a week (Chinese New Year is slowing down shipping times a lot), so keep an eye out if you can wait that long!
I've seen a lot of issues with the Note charging ports physically coming off of the board. I would open it up and make sure it's connected well. You can buy a replacement charging circuit board - they run about $7-15 and try it. That would be the easiest solution, and would likely fix any issues. If that DOESN'T fix the issue, then you have real problems.