My 2008 Gio ATV just buzzes when I start it
 

So I have a 2008 Gio ATV which was running fine, but the back shock broke so I had to replace it. While the back shock was off I kinda let it drop a bit (I was still holding it tho), and the back dropped pretty low. After I replaced the shock I tried starting it and... nothing. So I topped up the battery with a smart charger, and now it just buzzes when I turn the key. Same battery, wired the same, but now it doesn't start. What can the problem be, everything is exactly the same except the shock.

Sounds like the battery can't produce the cold cranking amps to fire up the starter. I would grab some jumper cables and test it on your car's battery.