If you're down on your bucks and need a good tip on where to find slightly used replacement parts, I've always found the local junkyard to be a great place to hunt. It never fails, on any given day I can wander into my local self-service wrecking yard and find an old truck or car that's loaded with an assortment of new carburetion and ignition parts. It's not hard to figure out what's going on, the junked vehicle's owner was chasing a ghost and bought a lot of unnecessary parts before he gave up trying to repair the problem and accepted defeat.
This was pretty much the scenario for the '56 Ford F-100 I bought a few years ago. Sitting idle in a garage, the '56 hadn't been started by the original owner for five or six years before the middleman I purchased it from had tried to get it up and running again. Eventually, after throwing new spark plugs, plug wires, points and condenser, distributor cap, fuel pump, and boiling the gas tank clean, he finally got the truck to start. When I was looking to buy the '56 the middleman demonstrated to me that the truck ran, but explained the engine could die and not restart at any moment.
After spending a lot of time establishing that the ignition and fuel systems were up to specification I tracked the intermittent ghost to a fuel line between the tank and cab floor that was crimped when the gas tank was reinstalled. After the rubber fuel line heated up and had been subjected to fuel pump suction it would collapse and shut off the fuel supply. I changed the fuel line over to a high-quality, high-pressure fuel injection-rated hose and the problem went away. The 272-inch Y-block engine never missed a beat. That was the case for a couple of years when all of a sudden the ghost returned. Just the same as before, the engine would start up and die, until eventually it wouldn't restart at all.
According to most repair manuals the odds are always in favor of a dead engine problem on an older vehicle can be traced to an ignition failure as opposed to fuel. That said, if the engine turns over but doesn't start it's a good idea to make sure the gas tank isn't empty. Once it's established that there's at least a few gallons of fresh gasoline present the next step is to look for spark. This can be done by pulling a spark plug, grounding it to the block, and cranking the engine over to see if the plug has a good, strong spark at the electrode. One of my favorite ways, and fast too, to determine if the problem stems from the fuel or ignition system is to spray starting fluid into the carburetor and then start it up. If the engine runs a few seconds and then quits it has spark, so that means there isn't a steady supply of fuel. The next step is to go right to the source and test the fuel pump for sufficient pressure. In order to run properly a carbureted engine needs between 4 and 6 psi of fuel pressure. In the following photos I've included a few tips on how to ensure you've not only come to the right conclusion regarding your diagnosis, but you will be able to install a new fuel pump properly as well. And as an added bonus I've thrown in a few ghost busting tips.

To prime an engine, starting...

To prime an engine, starting fluid works better than gasoline for two reasons: it is more volatile and combusts easier. Plus it doesn't contaminate the engine oil as much as pouring gasoline into the carburetor does. If the engine runs briefly you're dealing with a fuel supply problem. If it doesn't run at all it means you have an ignition problem.

When attempting to start an...

When attempting to start an engine that has not run in years, leave the cooling system dry in case the head gaskets are leaking, which would allow coolant to leak into the combustion chamber and foul the spark plugs. After the engine has been started and the head gaskets are determined to be sealing, use a good antifreeze, such as Prestone, in a 50/50 mixture with water.

The delivery of fuel to the...

The delivery of fuel to the carb was weak and intermittent. Going on a strong hunch, I disconnected the fuel lines and unbolted the two mounting bolts to remove the suspect fuel pump.

The brand-new Y-block replacement...

The brand-new Y-block replacement fuel pump from Dennis Carpenter comes complete with new fittings, one new mounting bolt, and a gasket. I applied gasket glue to the pump side of the gasket only.

The most critical stage of...

The most critical stage of installing a new fuel pump is to ensure the fuel pump drive (cam) located on the camshaft is positioned at the lowest point of the cam (fuel pump not under load). A toothbrush can be used to feel for the drive cam's position.

Using a remote starter switch...

Using a remote starter switch attached to the starter solenoid on the firewall turns this into a one-man operation.

I used my left hand to operate...

I used my left hand to operate the starter switch while my right hand held the toothbrush against the drive cam to feel for the lowest point.

Grease should be applied to...

Grease should be applied to the fuel pump arm (lever) to ensure against scuffing or galling the arm and drive cam before engine oil can reach it.

I installed the gasket, fit...

I installed the gasket, fit the mounting bolts, and positioned the new fuel pump on the engine without brushing the fuel pump arm against any exterior dirt, grease, or grime.

With the mounting bolts removed,...

With the mounting bolts removed, moving the fuel pump up and down against the drive cam will actuate the fuel pump and emit a suction/pressure sound. Properly aligned, the pump will be relaxed and the two mounting bolts can then be reinstalled and tightened down evenly.

Before proceeding further...

Before proceeding further I tested the fuel pump with a pressure gauge. I cranked the engine over with the remote starter switch and obtained 6 psi at the outlet marked "out."

Extreme care should be used...

Extreme care should be used to prevent fuel leaks while installing the fittings. Thread sealant should only be used on the threads, and not on the double-flared fitting's face. The seal is at the double-flare and not at the threads. Sealing the threads will not correct a leaking double-flare.

Overtightening the fittings...

Overtightening the fittings into the fuel pump housing can crack the housing. Undertightening can produce leaks. Proceed carefully!

After cutting the new tubular...

After cutting the new tubular steel fuel lines I made, I reamed inside the steel tubing to ensure there were no obstructions.

Next, I used a sharp Nicholson...

Next, I used a sharp Nicholson file to dress the tubing ends. Free from burrs, the fuel lines slid on easily.

This style of hose cutter,...

This style of hose cutter, available from most auto parts stores such as Napa, produces a clean, even cut that even the most particular DIYer will admire.

The brass fittings were clocked...

The brass fittings were clocked at the best possible angle needed to accept the fuel lines. Again proper tightening is critical.

A flare-nut wrench, such as...

A flare-nut wrench, such as this one from Craftsman, should be used to avoid rounding off the flats.

With the fuel pump properly...

With the fuel pump properly installed, the next task was to lose the hideous yellow plug wires installed by the middleman. Note that the plug ends are angled.

Because I prefer to use Autolite...

Because I prefer to use Autolite spark plugs, I chose to use Autolite plug wires. Not exactly a good custom fit for a Y-block, the wires came in only two lengths. The four longest wires needed to be used on the engine's left bank.

Drawing my own reference chart...

Drawing my own reference chart with engine rotation, firing order, and spark plug location has always worked well for me.

In lieu of a good wire spark...

In lieu of a good wire spark plug gap tool, a feeler gauge can be used to measure the gap. Make sure not to contact any area except between the electrode. I used a hammer very carefully to close the gap to 0.35 inches.

Because the Y-block engine...

Because the Y-block engine uses solid lifters and the valve covers must be removed to adjust the valves, the fit of the Autolite spark plug wires creates a problem.

I did like how neat the angle-tip...

I did like how neat the angle-tip ends on the Autolite plug wires fit on the distributor.

It's too bad Autolite doesn't...

It's too bad Autolite doesn't use angle-tip spark plug ends. These straight spark plug ends are funky-looking to say the least.

I've always had good luck...

I've always had good luck with Fram filters, not the problems the Internet wizards always seem to gripe about. Changing the oil and filter after an engine's internals have been exposed to excess gasoline is always a good idea, I just had to make sure the oil had a ZDDP-type additive to protect the Y-block's flat tappets.