When you say '... charged and installed the battery...', did you actually check the battery voltage, &/or Load test it??
Spyders are
EXTREMELY power hungry, and when you try to start them, that power hunger/demand is at its peak, what with trying to crank the starter, turn on the electric Power Steering; start up a bunch of sensors and computers; maybe change a gear back to Neutral cos when you stopped it last you didn't select Neutral first; and more... All of that takes a
LOT of power out of what is really a pretty small battery, and even a brand new battery might not be fully up to that task,
ESPECIALLY if it wasn't initialised properly and charged on a proper charger for at least 8 hours before installation - was yours?? Do you really
KNOW?? Or are you just taking the dealer &/or battery retailer's word for that??
So the very first thing to check whenever this sort of 'won't start' thing happens is your battery!
Even if you just put a multi-meter across the terminals and get readings from when it's sat overnight with no load; then when you turn the ignition on; and then while you're actually cranking the starter; a reading if/when the engine actually starts; and finally, when you rev it up to about 3500 rpm. If you get (or try to get) those 5 readings, and you can't or the voltage
EVER drops anything much below 12 volts, then it's likely that your battery is the problem! If you can get it properly load tested, so much the better,
but a response from the tester of,
"Nah, it's not the battery, cos it shows it's good" is NOT GOOD ENOUGH!! You
NEED to
know if the voltage ever dropped below 12 volts, and not just the 10.7 volts that
USED to be considered an acceptable minimum for a 'Good' battery back in the days many load tester devices were designed, the testers were trained, and most engines electrical systems only had to drive the points, plugs, a single coil, and maybe a radio!!
Your Spyder uses a HELLUVA LOT more power than that, it's likely the fuel pump alone drags more juice out of the battery than all of that on a pre-EFI engine, while your Spyder has all those computers and sensors and Dynamic Power Steering Systems and multi-point fuel injection with high draw coils and spark plugs and computer controlled electro-solenoid gear changing and more!! So if your battery can't push at least something
very near 12 volts ALL the time, you're not likely to be able to start it; and even if you can, it probably won't run for long &/or too often, not unless your charging system is really in top notch condition and you can ride it for more than the 30 mins or so minimum without stopping that it'll take just to put back the charge sucked out of it by just
ONE start!!
So check your battery FIRST, and if it's not up to the task, you can
try charging it properly, but having once failed, it
WILL do that again, probably sooner rather than later...

If it fails the 'holds at least 12 volts all the time' test and you want to save yourself some time, money, and maybe even save yourself from being stuck out there somewhere with a dead battery, miles from home/any help, then cut to the chase now and get yourself a new, quality AGM battery with
at least 350 CCA and 21 A/hr capacity (or equivalent if you go for one of the nickel whatever types, just make sure you've got a suitable Ni charger!) and then make sure the new battery is initialised and charged properly
BEFORE installation; and then after installation, check that the voltage never drops below 12 volts during the (attempted) start cycle. Then, and only then, can you really go searching for any other problems (maybe check out the connections on the ignition tumbler, that 'pop (or snap)' sounds ominous!) but without ensuring the battery is up to the task
FIRST, everything else is a pure stab in the dark and could mean you're just wasting time and maybe money on other things when it could be the battery to start with

(or not, if it still won't crank!

)
Just Sayin'... again!
