just got my hands on a 87 350 fourtrax for a great price, knew it had what seems like carb issues. would idle and run great until it got good and warmed up then start to bog down and lose power to the point of 1 gear to the handle was required just to crawl up an incline.so i pulled the carb and sure enough found the choke plunger cracked off inside the carb.also found there wasnt an air filter on board just the mesh...so i made a filter and left the choke out now it just runs like crap completely....so could the filter and choke be the root of my issues? or am i in for something else? i have to wait until tomorrow before i can order parts. i think im gonna get a new spark plug and fuel filter as well...not sure what the previous owner did....noticed my needle jet dosent go completely in and the slow jet was blocked a little..also the hole between the black plug and pilot screw, i cant blow any air through it, not sure if its suppose to be like that or maybe blocked.have some pics of the carb here

 

also discoverd the plug is a dr7 not a dr8 and it wasn't gapped, next Wednesday before the choke and filter arrive and $120 for the 3 of it..bit much i think

 

A lot of these machines were run with the fuel indicator in the 'on' position. Have a look in the tank, or drain the tank, and run in the 'reserve' position all the time. This position will draw fuel from the bottom of the tank, and once you get the tank/fuel clean, you wont get the condensation build-up.

It just sounds like you need to clean up your fuel system, and the tank is the place to start.

 

funny enough the muffler was plugged solid...pulled it and ran straight piped like a raped ape...so i cut the end off and cleaned it out welded together and perfect

 

then the fuel pump gave out completely ...so after some tinkering straightened out and cleaned the contacts and a bad wire and on the go again