HI Jeremie, from your description, I agree with Ron also. compression test will also tell you which side. if its a sticky valve you can trickle ATF into the carb while its running. that process will generally clean up the valve stems. may take an hour or two depending on condition. you can also add lucas fuel additive to the tank at the same time. if its the exhaust valve it may take a little longer to free up.
I once started a 39 Plymouth 6 cyl. flat head that had been sitting 30+ yrs. 56,000 original miles. fired up on just 3 cyls. eventually!! took me 2 days and several gallons of fluid but she cleared right up and was still purring like a kitty 6 months later when I sold her. got her from the proverbial little old lady who bought her new and said she was running fine, when she parked her. good luck, J.Z.M.