+1May want to have the battery tested. I know it may sound weird but G4.5 Taurus (04-07) get really cranky when the batteries get weak. Hence they do weird things. Mine would intermittently not want to start. I had to cycle the key several times before it would start. I originally thought the same thing as you: fuel pump. I load tested the battery and it was only putting out 345 CCA! Replaced battery exactly a month ago, no problems since.
Had same problem for about a year and it was the battery. Cranked fine but would not fire up.