Ditto to what Jerry said
Sounds like yours could be a few things.
As all the others said,
1. Replace those cloth covered fuel lines with good quality rubber ones (I replaced both of our 6420 fuel systems from tank up and back with good NAPA stuff)
2. Our `03 6420 was making a popping / snapping sound when running. Turned out to be air in the fuel being pushed through the injectors.
Had to replace the lift pump that sits on the left side of the tractor, about mid way in the frame, directly below the dipstick. The pump was bad, I imagine the inner diaphragm had a hole in it, causing air infusion in the delivered fuel. The replacement kit from deere was pricey, but it fixed the problem immediately. In fact, the replacement Bosch pump that they furnished (along with all necessary hardware, brackets, fittings, etc.) was about twice the size of the factory original lift pump. It seems to do a better job, and is also much more quiet (not that this matters). It barely fits in the space where the old one was.
Might as well replace the in-line check valve as well. On 6420`s they are located just prior to the inlet side of the first fuel filter.
If you are going to replace all the lines, including those that go to and from the tank, there is a trap door in the floor of the cab which allows easy access to the top of the fuel tank. Just lift the rubber floor mat out and you are in good shape.
Good luck! Keep us posted