@Lod 10
If the TV has a USB port built in
(I'm almost betting it does)
You may need to get a PS2 to USB adapter or some kind of USB controller, like a PS3 controller.
Not saying it would 100% work, but it's worth a shot. Since you mentioned the TV doesn't have Bluetooth
(I've never seen one with Bluetooth, but that's not the point) again, a USB adapter for your original PS2 controllers or a wired PS3 controller would likely work.
I assume the TV is running some version of Android, so it should have drivers for either controller type PlayStation or Xbox. If it's Android, you might be able to get a Bluetooth dongle and connect that way. Again, I don't know the make or model of your TV... its OS etc.. so these are just shots in the dark.
And is that a PS4 controller? You might be able to hook it up via the charging cable to the USB port in the TV
(again I'm assuming it has one) and it may connect that way.
Worth a shot