Wifi not turning on

For most all Samsung models the WiFi and Bluetooth share the same chip. This chip is generally located right above where the SIM/SD slot is located. I'm not exactly sure how damaging the slot would have done anything to that chip unless you tried changing the slot yourself and fried the chip that handles the WiFi. I've personally never fixed any of these due to the chip being epoxied in, at work they tell us just to trash phones with this failure. But whether or not a shop would have the ability to fix that, who knows, more power to them if they can.

For starters I would try a factor data reset on the phone and/or re-flashing the phone's software. It's a small chance, but it's worth taking before paying anybody. And if you have to take it somewhere to get it fixed, just know that this phone is quite old, it might not even be worth fixing anymore. For what they'd charge you, you could almost go out and buy another one.