When you turn the key to the 2nd click, the dash lights will come on, you will hear the pump buzz for about a second.

If the PATS has not recognised the key or it has a fault, the dash lights will still come on on the 2nd click, but the pump will not prime, the LED above the clock will flash a fault code, and it will not crank over when turning the key all the way.

I'd be checking and cleaning the earths under the air box next. It could even be a dead cell in the battery.