Pontiac Grand Prix starting issues

Hello,
My daughters car has an intermittent starting
problem. The battery measures 13.4 volts
and is fairly new. Sometimes when the key is
turned, the dash and head light turn on, but
there is no attempt to crank the engine. Other
times, the engine cranks and then starts
roughly. Some times it starts with no issues
at all. I suspect the fuel pump is or is going
bad. I suspect there is a fuel pressure switch
that tells the car that the fuel system is
pressurized before cranking the engine. Can
you confirm my suspicions?