The bike shop won't fix my newly bought bike
Your new bike doesn't work properly: of course this isn't normal.

At this point, your best option is surely to return the bike to the shop for a full refund and buy a new bike from somewhere else. If there are no other Trek dealerships nearby, buy another brand.

You exact legal rights in this situation will depend on where in the world you are but I would expect that the right to return faulty goods for a full refund should be pretty much universal. One would hope that the shop will just accept your request for a refund. If they don't, you'll need to find out about your rights, and maybe ask on Law Stack Exchange.