If you have any question as to the integrity of the fuel lines REPLACE them. A loose fitting, clamp or hose will also keep the pump from pumping by allowing air to be sucked in.
The crud in the tank could also get into the check valves in the pump also reducing pumping action. Some tanks will have access to "snake" a tube into the tank "below" the pick-up tube to suck out the crud.
The carb sounds like it may be OK as it starts when primed.
Dave Neptune
