273 won't start regularly

I am a novice at engines, and I have a problem with my 67 Barracuda's 273. It has worked fine, always starting with the manual choke closed, and recently I took my daughter for a ride and after stopping at the grocery store for 45 minutes, it wouldn't restart. The first time I tried to restart it in the parking lot, I got one or two combustions and then nothing, just the engine turning over. After towing it home, I checked the following:

1. Fuel-
filter and line not clogged(disconnected fuel line at carburetor and saw gas squirt out of fuel line when I turned the engine over)
fuel flows into carburator. (After trying to start it, stepping on the gas causes gas to squirt into the carb.)

2. Fire-
checked plugs to 1 and 2 cylinders and spark present

3. Timing-
set harmonic balancer at timing mark and 1 was at TDC, as far as I could tell with a feeler placed through the removed spark plug. Also, rotor was lined up with contact for 1st cylinder on the cap.

So I tried pouring a little gas into the carburetor and starting it, but nothing happened. Ran out of time, so I stopped for the day.

A few days later, I took off the distributor cap, disconnected the fuel line again just to look at things again, put things back together, put a little gas in the carb, and it started after a single loud backfire type noise and I ran it for 20 minutes smoothly. I then turned the engine off, and tried to restart it- again one or two combustions but then nothing, except I ran the battery down and the started started turning over slowly, so I stopped for the night.

Today, I switched the battery to a fresh one, and it started (didn't pour any gas into the carburetor). Again, after running for a few minutes, I turned it off and tried to restart it but nothing.

Again, I am learning as I go, but any help or suggestions would be greatly appreciated. What should I do next? Please bear with me since I am a novice at this type of stuff, but very motivated to learn.