TYPO
Model should be 358.350830

Has the saw been setting or stored and not used for awhile??? If the fuel lines are deteriorated most likely the carb. diaphramn and rubber parts are going south also or at the least the small passages in the carb. are gummed up and blocking or reducing fuel flow.

Before tearing the carb. apart I would try this first. Sometimes when you change fuel lines air is inducted in the system and sometimes vapor lock occurs blocking fuel flow. If you are sure all the hoses and filter are good going to the carb. and back to the prime bulb (if that model has one) you can try to prime it with carb. cleaner.

Two ways of doing this. Initially prime by removing the spark plug using the red nozzle on the spray can of carb. cleaner squirt two second blast down the spark plug hole. With ignition switch off pull the rope couple times to clear the combustion chamber.

Install the spark plug, switch to on and pull the rope attempting to start. Should hit off the carb. cleaner after two or three pulls. If not try 1 to 2 second blast of carb. cleaner down the carb. venturi (opening with the throttle held wide open. try again. Should hit and run off the carb. cleaner for couple seconds. try this few times and maybe it will start pulling fuel up and through the carb.

If not probably have to dissassemble, inspect, and clean the carb. internal passages providing you know the fuel lines are good and connected correctly and the primer bulb (if has one) is not cracked creating vacuum leak causing the fuel system to suck air and now flow to the carb. .

Approx age of the saw, total hrs of use and how long did it sit until now with fuel in it? Have you or anyone gone into the carb to ck diaphragm, trash on and below fuel screen and in all passages? Have you checked to see what chainsaw the Craftsman is (they put Craftsmen on so many brands name chainsaws. Once you know who's saw it is you should be able to find good Youtubs and Text info on cleaning and rebuilding the Carb and trouble shooting period.

It's too hot in North TX to be cutting wood unless it's a must (be very careful). I know what you mean by storm damage in the area. I have been picking-up some nice small batches (10-20 sticks out of stacks). This is or was dangerous heat in minutes in the wrong time of day (just picking up wood vs any cutting/etc. It's causing me to spend too many hours behind this Monster vs getting some outside projects done.

Good Luck!