Ignition switch is a double-pole design, it switches two circuits. The main circuit carries the amps for a lot of stuff on the bike and it's been known for the solder jopints on those wires to come out of the switch, rendering the switch a not-switch. Replacing the switch is a PITA, so when mine went Tango Uniform I just cut those two wires and put an external switch on them. Still need the key to run the bike because the other circuit still has to be closed, but now I have two switches, the key and the "main."
Men more anal than myself would tear the whole bike apart and replace or repair the switch, but I just don't feel like doing that much work!
Initially turning the key on you should get brief fuel pump noise along with gauge sweep and LCD on, and tail and running light. No headlights. They don't come on until the engine starts.
So: do the gauges sweep and those other thing happen? Do you hear a click under the right upper cowling when you hit the starter button?
If the gauges sweep and lights come on but no fuel pump or click, then check the kill switch. Many bikes will crank but not fire with the kill switch set, but not the FJR. It will light the check engine light if you hit the start button with the kill switch set.
If the gauges sweep and fuel pump runs, but no click on the starter button, then either the button or the relay could be bad. Button is a simple momentary contact switch, might could be cleaned. Realy is harder to work on, because it's under the bodywork.
