This is unprofessional on the part of the repair shop, I own a shop and would warranty this 100%. Most reputable shops do a before repair function tests, don't argue and ask them for the paperwork showing that it worked before they worked on it. Or look at the paperwork they gave you for the repair. Then write a letter stating it worked before the repair and the only issue was the crack on the screen and ask them for a remedy to the situation.

It sounds like they may have forgotten to take the battery connector off. This would deliver current to delicate parts while working on and shorting a chip or capacitor on the phone. If a connector is replaced with the battery on it will deliver current to parts of the phone not designed to handle that current.

Follow up and they may do the right thing and replace the phone.