The snow blower works on chock more... however when moving thec chock to "run" mode it stops working...

Carb needs cleaning add 1 ounce carb/fuel inj cleaner to tank full of gas use unit will not hurt to run with choke on will be able to take choke off after 2or 3 tankfulls or pay someone to rebuild carb

As already suggested, you have a clogged fuel circuit. If adding carb. Cleaner doesn't work, you need to disassemble the carburetor and clean it out with carburetor cleaner and an air hose. Blowing out the fuel passages with the air hose is critical to getting it totally cleaned out.