Rebuild the carb -

Or if you prefer to piece-meal it -

First to check is the internal fuel filter, if it has one.
You could remove it temporarily to eliminate that as an issue.

Next, the float needle valve that could be 'varnished' closed.
If that's the issue, a full carb cleaning is probably needed.

Then check the accelerator pump shot.

Before disassembly, light hammer taps may free a stuck float valve.