from the problem you describe, it sounds like you have a bad switch.
so far, you are doing a great job diagnosing it. the next step would be to check the start button and on/off switch.
first, when you jump the wires on the relay, and all switches are set to "ON" and key is "ON" does it start or only crank the engine over without starting?
if the bike does start when you bypass the relay, the start button is most likely bad. if it does not start, the problem probably is your on/off switch
to test the start button, you will need to be able to access the wires for the button. you can either open the start button switch, or follow the wires to where they go to a connector. to test it with a multimeter, unconnect the switch, and put the multimeter leads into the wires THAT GO TO THE SWITCH. if you put the multimeter leads into the harness instead of the switch you will get a bad reading. place the meter on OHMS(looks like a horseshoe)setting and 10 range if not autoranging. with the button pressed and the meter leads in the wires, you should get 0 ohms. with the button not pressed, you should get OFL(OFFLINE), or no connection. if you get these results the switch is good, and plug it back in. if you dont have a multimeter, with key on and on/off switch on, you can jump the wires for the start switch. if the bike cranks over now, then you know the start button is bad.
to test the on/off switch, it will be the same testing procedure. the easiest way to test it is to set the multimeter on DC volts in the 20 range. place one lead on the wire that goes from the on/off switch to the start button. place the other lead on a good ground, like the battery terminal. if you have the key on and on/off switch on, you should get at least 10 volts on this wire. with the key on and switch off, you should get 0 volts to this wire.
test these switches, and i believe you will find out which is the bad component.