I was heading out of town car was running great, started acting like it was out of gas (has 3/4 tank) and would not start had it towed, the next day it started for about 7 seconds and then would not start, I had to charge the battery, so I tried the next day and the same thing. I'm not sure if the fuel pump is engaging but when I lock and unlock the doors it sounds like a fuel pump engaging, tried to see if I could smell gas at rail could'nt really tell,

 

Regarding the unlocking and locking - it's the sound of your trunk lock and unlock.



When my fuel pump broke. I was driving and then the engine turned off... then I was able to start the car 2-3 times, but nothing more. the engine ran for a few second and went off... then I could only hear my starter cranking and the car wouldn't start - it was the fuel pump.

So in your case, it's probably fuel pump.

P.S. I never hear my cars fuel pump working when i turn the key... unless I am outside by the gas tank.