(sorry, this is a partial, but combined repost of posts elsewhere, with added details, since i have yet to solve the problem)

I have an '02 ET4 that was just resurrected from dead storage. I replaced the battery and it started right up after 3 years. I rode it minimally for 3 days. Now it won't start. The starter turns over but the engine doesn't catch. I have replaced the high voltage coil, spark plug, fuel tap/line and have tested multiple components and everything checks out ok. So far, including spark plug wire/cap, starter motor, starter relay/switch, kill switch, immobilizer antenna, pick-up, stator, auto-choke, and maybe some things I have forgotten to mention. Admittedly, I have not yet cleaned the carb proper. I am using the "red" key and I cannot kick start it, since the transmission case got cracked after one too many frustrated attempts. The battery is fully charged and no success jump-starting, either. With each successive attempt at starting I must give the engine (where it meets up with the starter) some "taps" with a metal rod - after which the starter turns over, and turns, and turns, (ever slower) until finally, it stops, then the "click," and I repeat the process. The diagnostic LED indicates that the immobilizer is good and the scooter is capable of starting...BUT, and herein lies the crux of the problem, there is NO SPARK.

Any ideas/advice?
(Yes, the Vespa shop is next.)