6 weeks since the OP posted, and no news for over 2 weeks. The problem has existed for at least 3 months: in that time 'the dealer' kept it for a month and simply replaced the battery. The dealer also had no charger. The writing was already plainly on the wall in big bold letters. Then next visit they put a new battery on, rode it round the shop and said it was fine. If they suggested the OP's charger might be suspect, they should have tested it, and the OP should have insisted. Some dealer. It's still faulty.
It astonishes me that people spend a considerable amount on a decent product but can't see the wood for the trees when it develops a serious fault within the warranty period. As several people here have correctly said, early contact should have been made with Trek....but appears still not to have been made. Traders and manufacturers can't be blamed if they've not been told of a problem, and reputable ones are keen to put things right - that's what makes them reputable.
What more do people want?! Of course people aren't obliged to take advice, in this case from several who have given it, but it's crazy not to do so.