OldIHC

I got my rebuilt mechanical fuel pump back today and I just put it in my L-110. I have gas in the tank, I don't think there are any holes in the fuel line, and everything is good and sealed, however, the pump won't pump any fuel from the tank. I held the starter button down for at least 30 seconds straight and no fuel was coming through. So to ensure that the pump works I had a small piece of hose coming from the pump to the inlet line and I disconnected the hose from the line, put the hose in a bottle of fuel, and cranked the engine. The fuel pump pumped the fuel just fine then, so I hooked the hose back up to the line and tried again. Still nothing! Any idea of what I should do? Also, I noticed there is a valve on the part where the inlet line enters the fuel tank. Any idea what that's for?

Pictures help. Are you sure that the inlet on your carb is not stuck shut.

It's not that the fuel isn't getting to the carburetor, but that it's not even getting to the pump. I know this because I have a clear plastic in-line fuel filter on the hose going to the pump, and when there is fuel being pumped you can see it flowing through the filter.When I turn the truck over now you can't see any fuel being pumped through the filter.

On my truck, there was a screen on the pickup tube down in the tank. If the screen, or the pickup tube itself, gets plugged, you will have what you're experiencing.

My tank also had a shut-off valve, I suppose for tank removal, in the fuel line at the tank. If yours has one, make sure the valve is open.

Yes, I believe there is a shut off valve. Which way would be open, unscrewing it or screwing it in all the way? Would the screen be over where the fuel line enters the fuel tank?

If this were my truck, I would take that shut-off valve off and put it in the scrap for recycling. That is likely an older style valve and the design that can leak. I would replace the valve with a check valve. This will prevent fuel run-back into the tank. The other benefit of a check valve is having the fuel at the carburetor fo an almost instant start.
It should be understood, the fuel pump does not "suck." The pump lowers the pressure in the fuel line by pumping the fuel toward the carburetor and this leaves a lower pressure behind the pump. It is the atmospheric pressure that pushed the fuel along to the pump.
If the fuel pick-up tube in the tank is compromised by rust there could be a corrosion hole and it is likely the rust has partially blocked the inside of the tube.
Replacing the fuel lines from the tank to the pump and beyond to the carburetor should be one of the first "to-do" important repairs.
Something else to check for is, floating debris in the fuel tank. In times past, it was very common to poke a shop rag into the fuel tank filler tube when the gas cap was misplaced. It was common for the rag to fall into the fuel tank. Every now and then, the rag would obstruct the fuel pick-up tube and the engine would stall or become intermittent.
Do not entertain the possibility of changing to an electric fuel pump until you replace all of the fuel line. Can you say FIRE

I can't find where to buy a new fuel line for my 1950 L-110.

The fuel line is just mild steel line. It is the same as is used for brake line. NAPA sell the line in straight lengths and in rolls. If NAPA is not your preferred place to shop, go to the closes other auto parts store. If these resellers do not work for you, AMAZON is another option.
Measure the outside diameter of the original fuel line so you will know what to ask for.
Unless you have spent about $800, as I have, on specialty tubing tools to form stainless steel and mild steel line/tube buy the steel line.

Pre-bent fuel and brake lines are made of unobtanium for these trucks. As I just posted to another newbie, a tubing bender is a good investment when working on these trucks. So is a flaring tool.

Turning the valve counterclockwise opens it.

The tube that goes into the tank has to come out to find the screen...if it's still there.