This whole "we'll come out next Sunday" business is a load of BS, bring the TV to them. Call a friend to help you pick it up. Take it there. Bring it in their shop. Make a scene. Yell. Courteously, I don't know how Mexican police can be but hopefully it's a busy, populated area. If they won't give you satisfaction of a properly working television demand a refund. Surely there must be something like a Better Business Bureau de Mexico. You don't have to be violent, just make clear that you want them to provide what you paid for, even if you're willing to accept that "it wasn't like this when it left the shop," offer to pay for that "repair," this is pretty much your only hope of getting this TV fixed and fixed properly.
You are damned if you do and damned if you don't. If you really can't manage to move the TV into your car and back into their shop, you are just as screwed as if you cannot get a new TV into your car and back into your home.
Somehow, I definitely think that one of those two is a better option for you, however.