Cole, I think the TRS is actually an Ariens produced model for JD. Mr. Deere is very secretive about his walk behind snowblowers
Engine nomenclature would help (Tecumseh, Briggs, LCT???)
A picture could get some more response? Are you having trouble starting it now, or are you stuck in the belt area? If you are "burning" belts it may be as simple as a spring coming off the auger brake, or a seized auger idler pulley.
The primer should, and will, pump gas out of the carb if pushed a few too many times. Not bashing you, but if you're burning belts, the engine is running fine, correct?