If the carb was stored with fuel in it, you may have clogged the vents in the low speed circuit and also the power valve. Not likely clogged on the main jets. even if it was stored dry, I have seen stuff get into the jets (low speed jets/vents are very small) and that would lean you out causing the issue you are talking about. It does not sound like the accelerator pump is your issue. It works and would take a lot to flood the engine which then would be hard to start right back up without some excess cranking.