Thanks, Red, et al, for your safety concerns. I'll wear my vinyl gloves in the future...
NAPA tested both my batteries (the original and my newer Yuasa). Both tested fine.
So, the fact I'm not getting any kind of turnover when trying to start the engine, is not due to the battery. Could it be my trickle charger is defective? Or (more likely) something's wrong in the scoot?
Any simple tests I can do to know for sure what the problem is, or is it time to give more money to the mechanics?
If you've hooked the battery back up, verified it has charge, verified that your power switch is on, & tried gripping both brakes (to verify it's not just one switch in them), you're down to a wiring issue or a bad starter. Either way I'd take a look at the starter, & make sure it's wired properly, maybe even try to jump the solenoid just to see if it spins (make sure bike's on center stand, & that you don't ground yourself).
Beyond that you're looking at switches I'd figger.
And just for the sake of argument. How old is your battery? If it's more than a couple years you may want to consider a new one anyway.
Won't hurt unless ya spill acid on yourself while filling it.
(of note if ya get one like I tend to buy you would need a charger, probably a bit more aggressive than a .75 float charger)