Crank and no start is my absolute favorite to diagnose/follow!
This issue is the one time where you HAVE to be VERY detailed in your diagnostic procedures!
Let's start with the basics....
1. Do you have spark at atleast 3 of your spark plugs and ignition coils
2. Do you have good fuel pressure at the fuel pressure port, near the engine
3. Are you getting air into your intake and does your intake flap work/move with pedal operation
4. Has anything else happened recently to point us in a good direction to help you
5. How long have you had the P0403 error code
Possible items that could be broken/bad:
1. Bad fuel pump
2. Bad ground
3. Bad relay/fuse
4. Clogged fuel filter (depending on the year of your vehicle)
5. Bad Fuel injectors (probably not the issue though)
I assume the grounds are the same for the 5.3 as the 4.2. I would check the two grounds on the outside of the frame near the driver's door and passenger's door. There is also one on the outside of the frame, in the driver's side front of the vehicles (this one is very prone to corrosion).
I would then check the plug going to the EGR itself. Make sure it's clean and not corroded. I would spray the plug and plug socket with an electrical cleaner as well. If the code doesn't clear, I would try to clean the EGR valve or just replace it. Realize that replacing the EGR valve may not fix the problem and you're looking at possibly having to replace the fuel pump. Which could cost $200-$400, depending on where you purchase it from.
Going on MRRSM's instructions:
Have your GF/Wife/Buddy stand at the rear of the driver's side of the vehicle and listen near the ground as you turn the key on (do not attempt to start it, just turn the key on position) and they should hear the fuel pump prime for about 2-3 seconds. If nothing is heard after a few attempts, then try and hit the bottom of the fuel tank with a rubber hammer a few times and attempt to start it again. If it starts then you probably have a bad fuel pump.
If it doesn't start then you could still have a bad fuel pump but, I would check for power at each pin of the relay, using MRRSM's link he provided from MAY03LT.