OK the throttle slide. When the carbs have been sitting for a long time they accumulate a lot of old varnish that is almost like glue. You can try running very hot water down into the carb and also squirting some strong detergent in it.
After that try some wd 40 or penetarting oil. See if you can go in from either side with a long thin flat blade screw driver and gently try to pry the throttle slide up. Keep repeating the hot water flush and the oil. It will eventually work loose.