When your Garmin Nuvi 350 shows the error message "System Software Missing"
Download and extract 060404120315_nuvi_sys.zip to a dedicated directory.
After this procedure, your Nuvi 350 should be version 3.20. The Nuvi unit will be "factory reset", so you might have to customize it to your preferences.
You may now upgrade with later versions, for example 3.30 and 3.60. If you have a slow Internet line, don't use Garmins Webupdater. In stead, download the file for manual updating the unit !
Also see the Aasli Forum regarding GPS and Garmin