Are you sure your power supply is working and is properly plugged in? Does the wheel turn itself when you first power the PS3 on with it plugged in? Because if the supply isn't working and the wheel doesn't calibrate itself, it won't steer but everything else will work.
If you're not sure whether or not the supply is working, I'm not really sure what you could do to test it. If you've got a multimeter you could put it on the voltage setting (NOT the current setting, that is very important), place one probe inside the barrel plug and touch the other on the outer metal part, and see what it reads, and if that's close to what is printed on the supply itself then it's working (obviously). Other than that I suppose you could check the wire for cuts, pinching or general signs of wear but if the wire has been severed inside the insulation it's going to be difficult to tell as it'll look ok from the outside.
