AFAIK Kohler uses a rubber, or i've heard illengine call it a Viton tip, no seat in the carb, so it just a soft tipped needle to replace. But that all depends on the carb Mfger.
Post the engine model number, should be on a shiny silver tag on the plastic engine cover. If the gas tank was completely empty then i suspect some got into the crankcase, by new oil an filter.. sometimes you'll have to change the oil and filter a time or 3 to get all the gas out... i went through that with my courage 19 last fall, i bought 4 quarts (2 changes worth) of cheap Havoline oil, fire it up, run it a bit, shut it down, change the oil and filter, fill up with more havoline 10-30, run it a bit, change it, then i poured in Valvoline 10-30 and its been good since.