In all honesty, it's your fault for buying a third-party non-PC controller that's neither built for PC, nor an official PS3 controller.
You can't expect Ashley or us to fix something that's not built for the hardware you're trying it use it on, let alone programs on said hardware.
The controller you posted a pic of is a cheap copy of a PS3 gamepad, doesn't really matter if it's new or not. I once bought a Chinese PC controller based on the PS2 controller and several buttons didn't work, thankfully I got refunded.
Just PM'ed you the DS3 I use. If you're not able to use it then you have a bad controller, since I have two Dualshock 3 controllers (both are different models from each other) and they work perfectly with it.
In any case, if your purpose for using a controller is to use it on a PC, buy an official PC controller from a legitimate source.
Third-party cookie-cutter items can only damage your computer and cause you headaches.
Let me know if the DS3 I sent you works. If not try to get a refund on your controller.