Well, to get it to fire, you have got to have the right fuel air mix, good compression, and a hot spark at the right time.
First of all, make sure you are using NEW GAS.
Then I would do the following;
Get a compression tester, Pull all the plugs and test each cylinder. Do this yourself and have your buddy work the starter. Write the values down for each cylinder.
Pull the boot back from your plug wires and make sure each wire has a good hot spark off the block.
Check the timing by static timing the engine, remove the plug from number one cylinder and make sure the piston is at TDC when it is supposed to be. I put a piece of plastic covered wire through the plug hole 'til it touches the top and rock the engine back and forth to find TDC.
Pull the air cleaner and look down into the carb and work the throttle. You should see/hear/smell gas.
If all this checks out, I would look for vacuum leaks at the manifold and at the vacuum advance. If this checks out, borrow a known good carb and try it again.
By the way, sometimes stupid stuff happens like a batch of bad spark plugs. I had a similar situation to yours in my '51 burb a few years ago. It stopped running and starting well, and I found the vacuum advance was bad. Replaced it, and took the opportunity to replace the points/condenser and plugs. I could not get it to start and run for the life of me. Finally (months later) I though, what the hey, lets try new plugs.
Started right up on the first crank.
Kurt
