Charged battery, but doesn't even try to start.

If I had a nickel for every 'good battery' that turned out to be junk after replacing starters and switches.... I'd have about $17.50 - but still, that's a lot of junk batteries.
My first battery check is always: turn on headlights, try to crank. If headlights never come on - bad battery. If they're dim and go out when you key it to start, bad battery. Could also just be a bad connection either at the battery terminals, or ground wire.

If the battery is good, then I'd be looking at the neutral safety switch circuit which can interrupt power to the starter relay. I'd also make sure the positive wire from the battery to the relay and from the relay to the starter isn't compromised. I've had clutch linkages smash mine and cause a dead short which stopped the starter from cranking with the clutch in. Trying to jumper 12v from the battery to the start terminal on the relay will help you figure out if the key signal is getting to the relay. A test light or multi-meter can do the same, if you have them.