If you don't have a voltmeter, this might be a good time to get one. As with all electrical problems, you want to trace the circuit until you find the issue. In this case start at the battery, then check the starter relay. Does it have both 12V power from the battery and is it getting the start signal when you press the start button? If not, check the relay itself, you can take a jumper wire, a fused one is best, and apply 12V to the relay coil. The solenoid should activate and the starter should run. If not, then you have a bad relay or if the relay activates you have a problem with the circuit to the starter. Just keep tracing until you find the fault.
A wiring diagram like that in the service manual is very useful here especially if the issue is in the starter interlock that keeps the starter from running except when all the right conditions are met.
2005 GL1800 Silver