Since the starter doesn't work at all, no click or anything after 20m riding I'd suspect the starter solenoid. Your starter may have the solenoid integrated with the starter.
Check for loose connections to the battery and especially the ground cable.
A weak battery that is cold may start the bike, but when hot there is too much resistance and not enough current to trip the solenoid. A nearly dead battery can fool you, because they charge up easily to about the correct voltage, but won't put out enough current to turn a start motor. If the solenoid doesn't trip nothing happens. They're designed this way to protect the starters. But it's a pain when the battery is weak because sometimes it works and then leaves you stranded.
Fourth gear rattle - it may be that in fourth gear whatever is loose rattles because the resonant vibration is at just the right frequency. So, this may or may not be related to the starter problem.
Check for loose connections to the battery and especially the ground cable.
A weak battery that is cold may start the bike, but when hot there is too much resistance and not enough current to trip the solenoid. A nearly dead battery can fool you, because they charge up easily to about the correct voltage, but won't put out enough current to turn a start motor. If the solenoid doesn't trip nothing happens. They're designed this way to protect the starters. But it's a pain when the battery is weak because sometimes it works and then leaves you stranded.
Fourth gear rattle - it may be that in fourth gear whatever is loose rattles because the resonant vibration is at just the right frequency. So, this may or may not be related to the starter problem.
