When I turn it on everything goes to the left

I had this happen to me once before. Something's inside the PS3 joystick. Either that or something's screwy about the joystick itself. I never got around to fixing mine, but if you can you are certainly welcome to. I narrowed it down to replacing the joystick rotor itself, which means pulling out the soldering iron.

Another thing you can try is cleaning the contacts in and around the joystick itself with 90+% pure Alcohol cleaner. It helped me for a bit, but it wasn't permanent.

Alternatively, buying a new controller saves a ton of hassle. Just make sure to save the battery from the faulty controller - I use mine to test LEDs.