1999 Ford Taurus 1999 Ford Taurus No Start

I am having a very similar problem to this posting and was frustrated when the end source of the problem and fix wasnt updated.

Ill start from the beginning and giving a bit more information. I have a 1999 ford taurus lx with a vulcan v6 in it. The car has run perfect for the 1st 115000 miles. I was recently deployed to afghanistan for a year and while I was gone the car wasnt driven very much, because a bad coolant cap my wife thought it was "unreliable." I have since taken care of the coolant issue and am now having problems with fuel system.

The problem began when I was flushing the coolant. I shut the car off and went to restart it after I drained and refilled it and it would crank and not start. I waited until the next morning and it started without hesitation. The car ran fine for a week then I was going golfing and stopped by a gas station and came out to start and same thing. I went and golfed and came back and it started again without hesitation. The 3rd time happened was 2 days after that. I started reading up and troubleshooting. I changed the fuel filter first thing. I noticed when I was doing it that no fuel came out of the schrader valve. I attempted to start and again crank and no start. I started reading more about fuel pump. I then noticed that I wasnt hearing an audible hum from the fuel pump when I turned the key to the on position. I then thought the relay might be bad. I tested the relay and thought it was bad. I changed the ac clutch relay and fuel pump relay and I heard the fuel pump and it started. I went to advance and got a new relay and it ran good for a week. Then it happened again. I waited an hour and went to start it again and it started up. I drove home and as soon as I shut the car off I turned the key over and I noticed the fuel pump was working. The car sat 2 days and started fine the next time and I drove to my sons school and back and after that Im back to no starting.

Im kind of at a loss on where to go now. I guess it might be the fuel pump, but when the car is running I have no other symptoms such as stalling, spurting, or loss of power. I havent had a check engine light on at any time during this problem. Do any of the any of the sensors, i.E. Coolant, crankcase, etc. Tell the computer not to send power to the fuel pump?

Any suggestions.