I encountered a few of these at a small engine repair shop I worked at. The main thing for winterizing (or in this case summer-izing) that is storing them between seasons is to cut fuel flow and run the blower until it dies. This will starve the carburetor and prevent water build up and the fuel from turning to varnish. In my experience even with Stabil added it can be hard to start the next season and we recommended to our customers to simply drain the fuel system for storage. Fuel these days has so much ethanol added even with higher octanes I've have seen it start to turn to varnish within weeks and even high octane no ethanol blends are not recommended to be used after 3 months unless sealed (per STIHL guidelines). The reason is that the fuel can absorb moisture and build up water when exposed to the atmosphere and even a sealed tank can obtain moisture through heating and cooling cycles if it is stored in a garage, shed or warehouse.
The best bet if these steps weren't followed is to just drain the fuel system and start with all new fuel at the beginning of winter. If troubles persist a carburetor cleaning may be required.
As for having to tap the starting motor it may have loose connections or be going out. I had to replace a handful of them as moisture from the snow or vibration can start knocking things loose or corroding connections, something to keep in mind if it keeps giving you trouble.