Engine off and gas in the carb, make sure you see a squirt of fuel go down the throat of the carb when you open the throttle fairly quick.
The accelerator pump (dashpot) is exactly what is engineered to prevent what you describe.
Not sure what carb you have, but if a required check ball isn't in the right spot, or spots, the accel. pump won't work. Some have linkage that has to be on in the right direction or it won't work.
General mechanical ideas that apply to most carbs.
This may be yours...it is a Rochester 1 bbl carb. The Accel. linkage is in red. Make sure it is connected as as seen and moving when you open the throttle.
https://www.dropbox.com/s/y6418pvvhfz00lq/Rochester%20B1.png?dl=0Larry W.
