1999 Chevrolet Tahoe

Our Tahoe is a 1999 4door, 4x4. The engine is a 350ci, 5.7L V8 and the mileage is 104,400. According to the door label the model is K10706.
Yesterday we were driving home when the engine started to " cough" or " stutter", as if it wasn't getting fuel. My husband tried stepping on the accelerator, but there was no response. Later in the day my husband tried to start it. The engine wants to turn over, the starter is working and the battery is fully charged with clean posts. It sounds like it is not getting fuel. Stepping on the accelerator is not helpful. Again, seems like it is not getting fuel. We have experienced a week of freezing weather-unusual for our area of the country.
A little history. Last January (2006) we did a Do It Yourself replacement of the spark plug wires, spark plugs, distributor cap and rotor (at 99,000 miles). We picked up the parts at Napa Auto Parts. We had the dealer replace the serpentine belt. At 90,445 miles the dealer did the 90K service, and the fuel filter was replaced, a fuel flush was done and a new pcv valve was installed. An " engine fuel tune up" was done at 66K. We've followed the book with regard to servicing this car.
I am thinking that the fuel pump is no good, or a relay switch has failed. Perhaps the fuel line was frozen, got plugged and created a problem with the pump? At any rate, I am not sure where to begin, short of having the car towed to the dealer. If this was your car, what would you check, and in what order? And what would you be thinking as to what might be the problem?
Thanks for your help!
January 15, 2007.

1) check for burnt out fuses, and check to make sure the fuel pump relay isn't bad. Also check the fuel pump inertia switch. It cuts power to the fuel pump if it believes the car has been bumped too hard or you get into a wreck.
2) is the check engine light on? If yes, scan the computer for fault codes. That could give you a clue as to what's wrong.
3) check fuel pressure at the fuel rail.
4) check to make sure spark is reaching the sparkplugs by unscrewing them, plugging them back into the wire and holding them against a clean bare section of the engine bock while cranking the engine. You should get a series of nice sparks.
5)check compression in each cylinder and compare. The values should be fairly close to each other.

Those are the first things I would check. Basically all a vehicle needs to run is fuel delivered in the proper ratio at the right time, spark delivered at the right time and good compression on all cylinders. Fuel, spark, compression. And it runs. For some reason one (or all) of those are being partially or entirely withheld.

Jan 16, 2007.
Thank you for your ideas. Most of them are beyond our " skill set" and our " tool set", so we did what we could and then called AAA. I can't believe/understand this, but the guy asked if the fuel tank was full (it was), got under the car and beat on the fuel tank with a wrench while I tried to start the engine. It started! He said that with the combination of our unseasonably cold weather and a full tank he has started lots of Chevy trucks this way as of late. He also said " maybe or maybe not" when I asked if the fuel pump was going out. The engine service light is on now, but I don't know if it went on when we first had the problem on the way home or not. So my plan is to disconnect the battery and see if that will clear out the code, start the car, drive it around and see if the light comes back on. What do you think about all of this? Have you ever heard of this before?
Thanks for all of your help!

Jan 17, 2007.
: D I'm glad it's running now! No, I've never heard of beating on the fuel tank to get a vehicle running. I'll have to remember that. It sounds like beating on the fuel tank gives the fuel pump a jolt enough to get it going. I don't know if that a clue the fuel pump is going out or not though.

Disconnecting the battery to reset the computer should turn off the check engine light, however keep in mind that's not the prefered way of turning it off because it not only clears the codes stored in the computer and turns off the check engine light, but it also clears the vehicle's " learned" engine trim. It's perfectly safe though. And it will in NO way harm the vehicle. (To tell the truth, I sometimes do the same, because it thoroughly resets everything and sometimes that's prefered) The vehicle will exhibit some unusual driving charactaristics during the first couple dozen miles or so as it relearns fuel trim.

Jan 17, 2007.