I ordered a replacement for the charging connector pins you're talking about. However, when I removed the old one and put the new one in, there wasn't anything to 'adhese' it down with. But when I put it all back together it seemed to be snug and not move around. So I charged it and it did fine for a couple days until I was on the treadmill and, I suppose, sweat or condensation built up and got inside and the whole watch stopped working. I know it had a full charge before I got on the treadmill so something inside got affected. I've since taken the watch apart, hit it with a cool hairdryer, put it in a bag of rice and just tried to let it air out. All to no avail. It still will not turn on.
So my advice to you is to make sure you put some glue or something around the replacement to form an airtight seal.
Here's a link I found to the replacement part: http://stellatech.com/article.php?id=820524
Good Luck!