Don't you just love all that CA emissions junk that seems to surround the carburetor in a twisting mess of vacuum hoses? I sort of have the opposite of your problem. It ran sort of ok, but was very hard to start. I replaced everything you mentioned, but still ran lean, lean, and more lean. Nothing seems to correct it. I ended up having to replace the EGR Valve (nightmare to find), and completely replace the carburetor (impossible to find). I am still waiting for the carburetor to come from Florida, but this should solve all my problems. I tinkered with it for weeks, but finally bit the bullet and took it in for diagnosis at a local shop. It was worth it though, because the mechanic identified the problems in about 5 minutes and explained why each part was failing and how he could tell. $75 bucks for my peace of mind, and I learned a couple things too. I would bet that letting it sit for 3 years caused the carburetor to gum up, maybe the float is stuck. Maybe an idle jet is varnished over and plugged. Accelarator pump stuck open, who knows. Lots to go wrong in there. $189 for a completely remanufactured carb, very easy to change yourself, or less than one hour labor at a shop. importcarburetors.com is the best place I found.
On a slightly different topic, is your toy blue and white with tinted windows and a rear door?