I tapped around the carb and it started.
While doing so, I noticed fuel around the base of the carb and engine. Could the carb be leaking fuel?
Great! I have started many cars that have sat for awile by giving the carb a whack or two. Glad we were able to work this through together.
Your float or inlet valve is sticking.
Sometimes the inlet valve sticks open and you end up with flooding, or the float sticks down or fills with gas and you flood. That is not the case here.
In your case the inlet valve or float are sticking shut, so no gas into the carb. It will most likely do this again, especially if the car sits for longer periods of time.
You have a few choices at this time:
1. You can just replace the carburetor with a new one if you want. About $200 I think?
2. You can do a complete tear down, cleaning and reassembly. Installing new components and gaskets from a kit. Kits are cheap.
3. You replace just the gaskets and the inlet valve if you are not up to doing a complete tear down. This preserves your current settings.
My recommendation is that you do a complete tear down, cleaning and replacement of gaskets and parts. The standard carburetors are very simple. If you count the number of turns it takes to remove the idle mixture screw during disassembly you can get it back close to the original position before fine tuning it.
If you have never done this before let us know and we can give you some pointers and advice.
The slight wetness at the base of the carburetor is normal.
John