I procured a vehicle quite cheaply once because of a blocked fuel pickup line in the fuel tank. They had rebuilt the carb, replaced the fuel pump and the rubber fuel lines before giving up. It was a truck with the tank behind the seat, so I was able to remove the fuel level sender and pickup tube fairly easily, where I discovered the pickup tube was solidly packed with dirt for about 1 1/2 feet. I was able to get the truck home by cutting the line off and keeping the tank full of gas. Symptoms: the truck would start and run for about 15 seconds before quiting each time and wouldn't restart unless I waited a couple minutes. Long enough for the gas to "filter" slowly through the packed dirt after the fuel pump built up a vacuum in the fuel line, and refill the fuel pump. That gas would get pumped to the carb and allow the truck to run.
My handy tip for starting a car that has been sitting for a while or seems to be having fuel delivery problems is to put some gas in a small bottle and fill the carb fuel bowl up through the bowl vent tube. I find this works a lot better than pouring the gas down the carb throat, as it allows the engine to start and run for a while, sometimes long enough to get the fuel flowing properly through the lines and pump again. It also saves a lot of cranking and gets the engine running with a normal amount of fuel for idling, instead of washing down the cylinder walls. And I can usually get oil pressure pretty quick without jazzing the throttle to try and keep the engine running - bad thing to do with an engine that hasn't been run for a while.