We just bought a PS3 and we can't get the controllers to work. They aren't controllers that came with the system because it's used, and the controller it came with, is broken. We turned the PS3 off, plugged in the controller, and pressed the PS button. The 'Controller 1' light turned red, and thus, we know that the controller was assigned as controller 1. Then the TV had a black screen. I don't know what's damaged: The controller or the PS3. These aren't Sony controllers.
If you are starting up the PS3 for the first time, or in safe mode, it will need to configure its HDMI settings through your TV. Sony takes you through the steps on the startup screen. However, I think you must have a DualShock controller plugged into the USB port to advance.
The black screen may be the PS3 adjusting the screen resolution, but it may also be a loose connection, which could be an HDMI lead fault. Try using a lead you know works, wiggle it about a bit, or change the HDMI port on the TV you are using.
If you bought the PS3 from a store as "used", they have a duty to make sure what they are selling works including all peripherals.
This may or may not be useful. Just some thoughts.