Can you shift gears on the foot lever; ignition on, not started & see a difference in the gear display?
This quad is designed to start in neutral, so wont start till you see the N on the gear display unless you bypass the safety by pull in on the front brake lever on the handlebar, then hit the starter.
Does sound like you should check out the kill switch if it was damaged as it stops the ignition & fuel circuit from working. Including the fuel pump.
Also the headlight switch is in that block, so it may be shorting although that would blow fuses, sounds more like you need to check your connections inside the block or at the next wiring harness junction.
Also these quads have a rollover switch (bank angle sensor) which will stop everything, all you should have to do to reset that is turn the ignition off & on & you're good, unless it was a little corroded or gummed up, stuck in the cutoff position & needs cleaning/rebuilding. There is a thread on that, I think it's in repairs & maintenance.
EDIT; here is the service manual to help you solve problems,
http://www.mediafire.com/?ei8tb8n92lnawsu
Credit to sphill for sharing it with us,
http://www.hondaatvforums.net/forum...honda-atv-schematics-manual-help/6159-2007-2010-420-rancher-service-manual.html