Fuel pump sounds with 2001

I'm having problems starting my 2001 Silverado and I checked the common issues recommend on this site. I've since changed the fuel filter and checked the fuel pressure regulator, no fuel in the vacuum line that I could see. Here is what I noticed yesterday, when I turn the key on I hear the sound of the fuel pump priming the system and when it stops running I hear a hissing sound; it sounds like a tire leaking air. This is the only time I hear this sound and I'm thinking the pump is on it's way out.