Authorized repair service broke my phone

At an Apple Authorized Repair center I had my SE phone there to have the battery replaced.

On picking up the phone, the did'nt charge me for the new battery or labour cost but the phone is useless now as it won.t charge up past 40% and reboots itself every three minutes or so.

On complaining at the service center they said my phone had a bad logic board and that it wasn't there fault.

Before giving them the phone the only problem the phone had was that the batter only held a charge for 4 to 6 hours.

Who can I complain to about "the Authorized Repair Experts" and will apple do anything to support me.

James