Issues with phone repair in Phuket (Xperia z3)

Hi, 

I've had to get my phone screen for my Z3 replaced last week, the shop took longer than they said, and generally did a fairly poor job ("forgetting" to put my memory card back, which has miraculously changed brands from sandisk to another brand, the screen not fitting properly and letting light out the sides etc). I got the phone back friday, and as of monday morning suddenly it will no longer turn on. Plugging it into a charger makes a standard "charging" icon appear, which promptly disappears after a couple of seconds, the screen goes blank, and it starts over. I've taken this back to the shop, as i dont believe that its a coincidence, and suspect theyve swapped the battery. The shop want to charge me for a new battery and claim its completely unrelated to them. After going back and forth for about 20 minutes with them, theyve agreed to "have a look" but still havent agreed its their fault or admitted anything.

At this point, what are my options? Is it worth contacting the tourist police? Or the shopping centre itself as theyre based in Big C in Phuket. Any help people would give me would be great!

Thanks